Which president exercised the first veto?
April 5, 1792 — George Washington issued the first presidential veto of a Congressional bill today that introduced a new plan to increased the amount of seats for northern states in the House of Representatives.
Washington had a politically divided Cabinet, which proved to be no help in making the decision to veto.
In the end, Washington vetoed the bill on the grounds that it was unconstitutional to give some states more representation then others.
Sources
Words of Wisdom
I give my signature to many Bills with which my Judgment is at variance.... From the Nature of the Constitution, I must approve all parts of a Bill, or reject it in total. To do the latter can only be Justified upon the clear and obvious grounds of propriety; and I never had such confidence in my own faculty of judging as to be over tenacious of the opinions I may have imbibed in doubtful cases.