Since July 4, 1776, Americans have cherished the principles of “life, liberty and the pursuit of happiness”—but disagreed fiercely about how to apply them.

“I have never had a feeling politically that did not spring from the sentiments embodied in the Declaration of Independence,” President-elect Abraham Lincoln declared in Philadelphia in February 1861, standing in front of Independence Hall. The previous month, Lincoln had adapted language from the Book of Proverbs to emphasize to a Southern correspondent the place of the Declaration in his own thought. He wrote that “the expression of that principle [of Liberty for All], in our Declaration of Independence…was the word ‘fitly spoken’ which has proved an ‘apple of gold’ to us. The Union, and the Constitution, are the picture of silver, subsequently framed around it.”

Ever since it was adopted by the Continental Congress in 1776, the Declaration of Independence has been an almost sacred document in American life. Its influence on the way we think about politics and law is second only to the Constitution. In fact, as Lincoln recognized, the two documents are closely linked. From the Founding era until today, conservatives, liberals and everyone in between have agreed that the theoretical basis of the U.S. Constitution—and American political life in general—can be found in Thomas Jefferson’s most famous sentences:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. —That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, —That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it.

These principles have been invoked by Lincoln, Frederick Douglass and Martin Luther King, Jr., by advocates of women’s suffrage in the Progressive era and by modern opponents of the Supreme Court’s ruling on abortion rights in Roe v. Wade. Based on the philosophy of John Locke and the Scottish Enlightenment, these ringing words declare an enduring American consensus: that the purpose of government is to secure the rights of popular sovereignty, equality and liberty. But there’s a rub, and it is the source of our enduring disagreements: How are these inspiring ideals to be balanced against one another?

The modern divide between left and right can be seen as an ongoing debate about the relationship between the Declaration and the Constitution. Both sides rely on the idea that all people are endowed with natural rights—that is, inherent rights derived from God or nature, and antecedent to government. Liberals believe that the promises of the Declaration can be realized only with a powerful government that fights inequality, protects minorities and expands democracy. Conservatives, by contrast, believe that a powerful government poses the greatest danger to “Life, Liberty and the pursuit of Happiness” and therefore want a limited federal government that taxes and regulates less and defers to states and localities more.

Similar disagreements about the meaning of the Declaration can be traced through American political and legal history, from the Founding era to the Civil War to the New Deal.

The central constitutional debates in the early republic had to do with the question of where sovereignty lay in the new system. When the Constitution declared “We the people of the United States” in its opening sentence, did it mean the people acting as a single nation or the people as citizens of separate and independent states?

During the Constitutional Convention, James Wilson of Pennsylvania, one of the six men who signed both the Declaration and the Constitution, quoted the Declaration to argue that the new government should be seen as the creation of the American people acting as one. As Danielle Allen, author of “Our Declaration,” notes, Wilson believed, as he said on the floor of the convention, that the “colonies” had won their independence “not Individually but Unitedly.”

Decades later, Lincoln invoked Wilson’s vision of national popular sovereignty when he denied the constitutional right of the South to secede from the Union, declaring that since “we the people” as a whole had declared independence and ratified the Constitution, the whole people would have to consent before the Union could be altered. It took the Civil War to settle that violent constitutional debate in favor of the sovereignty of the nation.

The Civil War also decided a second constitutional question left open by the framers: If all men are endowed by their creator with equal liberty, how could the Declaration and the Constitution tolerate slavery? “The Declaration of Independence is the ringbolt to the chain of your nation’s destiny,” Frederick Douglass announced in his “What to the Slave is the Fourth of July” speech, delivered in Rochester, N.Y. on July 5, 1852. “The principles contained in that instrument are saving principles.” Women’s suffrage advocates also invoked the Declaration to support the self-evident truth “that all men and women are created equal,” as Elizabeth Cady Stanton announced at the first women’s rights convention in Seneca Falls, N.Y. in 1848.

In 1863, at Gettysburg, Lincoln looked back not to the Constitution of 1787 but to the Declaration of 1776—“Fourscore and seven years ago”—in promising a “new birth of freedom” of, by and for all the people. It took the 13th, 14th and 15th amendments, ratified after the Civil War, to enshrine the Declaration’s promise of equal liberty by ending slavery, establishing equal protection and due process of law for all persons and giving African-American men the right to vote.

How to secure these rights provoked immediate controversy. The Supreme Court thwarted the promise of the new amendments by striking down the Civil Rights Act of 1875, which promised equality in public accommodations, and by upholding segregation in Plessy v. Ferguson in 1896. In his “I Have a Dream” speech on the Washington Mall in 1963, Martin Luther King, Jr. said that “the Declaration of Independence and the Constitution were promissory notes” that had yet to be fulfilled. It would take the Court’s decision in Brown v. Board of Education in 1954 and the Civil Rights Act of 1964 to begin to make those promises a reality.

In the late 19th century, the Declaration played a central role in another debate, over the nature and limits of property rights. In 1884, Supreme Court Justice Joseph P. Bradley declared that freedom of contract was a natural right, protected from government regulation: “The right to follow any of the common occupations of life is an inalienable right; it was formulated as such under the phrase ‘pursuit of happiness’ in the Declaration of Independence.”

Bradley drew on Locke’s theory that “The great and chief end…of men’s uniting into common-wealths, and putting themselves under government, is the preservation of property,” ideas that influenced both Jefferson and Madison. From the Progressive era to the early New Deal, the Court invoked similar reasoning to strike down economic regulations championed by workers and labor unions, including minimum wage and maximum hour laws.

During the same period, populists and progressives invoked the Declaration to defend the expansion of government they believed necessary to make Jefferson’s self-evident truths a reality. In 1911, a year before being elected president, Woodrow Wilson told the Jefferson Club of Los Angeles, “If you want to understand the real Declaration of Independence, do not repeat the preface.” Challenging Jefferson and Madison’s vision of limited government, Wilson concluded, “Now, the business of every true Jeffersonian is to translate the terms of those abstract portions of the Declaration of Independence into the language and the problems of his own day.”

Wilson’s impatience with the structures and limits established at the founding laid the groundwork for the idea that made the Progressive Era and the New Deal possible: that the president is directly accountable to the people and can consolidate power in the federal government. Two decades later, Franklin Roosevelt invoked Jefferson, as well as his Progressive predecessors Wilson and Theodore Roosevelt, to make a similar argument as he sketched out his new constitutional vision in a 1932 speech. “The Declaration of Independence discusses the problem of Government in terms of a contract” to protect individual rights, Roosevelt announced. “The task of statesmanship has always been the re-definition of these rights in terms of a changing and growing social order.”

For Roosevelt and other New Deal liberals, the Constitution imposed few limits on the regulatory state. This meant that the president could rule by executive order, Congress could delegate broadly defined powers to the president, and executive agencies could pass regulations that affect all aspects of American life, from the economy to the environment.

Opponents on the right pushed back with their own interpretations of original principles. As Ken I. Kersch shows in his new book “Conservatives and the Constitution,” various strains of post-New Deal conservatives—including evangelicals, Catholics, libertarians and anti-Communists—invoked the Declaration to argue that the New Deal transgressed the original understanding of limited government. As Jill Lepore notes in “These Truths,” her new history of the U.S., most of the Declaration is a list of wrongs committed by the tyrannical George III. It can be read as a warning of the dangers of an overly powerful government and clearly influenced the framers as they established the separation of powers and the structures of federalism.

In a famous 1964 address that became known as “The Speech,” Ronald Reagan supported Barry Goldwater’s campaign for the presidency by declaring, “Our natural, inalienable rights are now considered to be a dispensation of government,” by which he meant the post-New Deal welfare state. Reagan believed that, rather than helping to achieve the promise of equality set out in the Declaration, the social welfare programs promoted by Goldwater’s opponent—President Lyndon B. Johnson—were an assault on the individual liberty and limited government set out in the Declaration and Constitution. When Reagan was elected President in 1980, he pledged to appoint justices to the Supreme Court who would resurrect the framers’ original understanding.

For some justices of the Supreme Court, the Declaration has remained a powerful lens for reading the Constitution, even if it often takes them in very different directions. Consider Justice Anthony Kennedy, who was appointed to the Court by President Reagan in an effort to roll back the post-New Deal regulatory state. Justice Kennedy’s Jeffersonian vision of limited government did indeed make him a reliable vote for certain conservative priorities, such as restricting affirmative action, striking down economic and campaign finance regulations and limiting government’s power to regulate health care.
On the other hand, he believed so fervently in the natural rights of equal liberty that he was willing to invoke a sweeping Jeffersonian vision of autonomy to uphold Roe v. Wade and to recognize a right to marriage equality. For Justice Kennedy, the self-evident truth that our rights pre-exist government empowered the Supreme Court to enforce rights not explicitly listed in the Constitution: “At the heart of liberty,” he wrote in upholding Roe in 1992, is the right to “define one’s own conception of existence, of meaning, of the universe and of the mystery of human life.”

Social and constitutional conservatives reject these expansive interpretations of the Declaration and offer rival views of their own. Justice Clarence Thomas invoked the Declaration in his dissenting opinion in Obergefell v. Hodges, the 2015 case that legalized same-sex marriage. “Since well before 1787,” he wrote, “liberty has been understood as freedom from government action, not entitlement to government benefits.” Other conservatives now cite the Declaration to lay the groundwork for a Supreme Court challenge to Roe, which they claim violates the God-given right to life. When Alabama legislators recently passed a law banning abortion, they cited the Declaration, saying that “from conception … all men are created equal” and possess a fundamental right to life.

And just last week, Justice Elena Kagan quoted the Declaration in her dissenting opinion from the Court’s decision that partisan gerrymandering is a question for legislatures rather than for courts. “Is that how American democracy is supposed to work?” she asked, citing the Declaration’s insistence that governments derive “their just Powers from the Consent of the Governed.”

Whether you are persuaded by Justice Thomas or Justice Kagan, it’s striking that the debate between conservatives and liberals on the Court continues to revolve around how to read the Constitution through the lens of the Declaration. How are we to balance its sometimes conflicting “self-evident” truths? That is the ongoing question of American politics and constitutional discourse.

In these polarized times, the fact that all sides still turn to the same profound statements of national purpose is no small thing. Our shared commitment to wrestle with the Declaration and the Constitution has always been a large part what it means to be American.

Mr. Rosen is president and CEO of the National Constitution Center in Philadelphia and a law professor at George Washington University. His new book, “Conversations with RBG: Ruth Bader Ginsburg on Life, Love, Liberty and Law” will be published in November.