The U.S. Constitution states:
"Every Bill which shall have passed the House of Representatives and
the Senate, shall, before it become a Law, be presented to the
President of the United States; If he approve he shall sign it, but if
not he shall return it, with his Objections to that House in which it
shall have originated, who shall enter the Objections at large on
their Journal, and proceed to reconsider it. If after such
Reconsideration two thirds of that House shall agree to pass the Bill,
it shall be sent, together with the Objections, to the other House, by
which it shall likewise be reconsidered, and if approved by two thirds
of that House, it shall become a Law."
"The United States Constitution" [Article I, Section 7, Clause 2]
United States House of Representatives
The text suggests that "every Bill which shall have been passed" --
regardless of the majority by which it was passed -- shall be
presented to the President, who may sign or return (veto) it. And
indeed, the Congressional Research Service confirms that the President
may veto a bill, and that a two-thirds vote to override the veto is
required, although "a measure may have passed originally by a large
majority vote in both houses."
"Congressional Overrides of Presidential Vetoes," by Mitchel A.
Sollenberger, Congressional Research Service (Updated April 7, 2004)
United States Senate
The same page of that report states:
"Congressional procedure and tradition, not the Constitution, have
determined that a vote of two-thirds of either or both houses of
Congress means a vote of two-thirds of those Members present and
voting (provided there is a quorum) and not, as is the practice in
some states, two-thirds of those elected."
"U.S. Constitution : Article I -- Annotations p. 24 -- Clause 2.
Approval by the President" [last paragraph: "The two-thirds vote of
each House required to pass a bill over a veto means two-thirds of a
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