Pew's most recent survey has reportedly found 63 percent of U.S. adults say the way the president is elected should be changed so that the winner of the popular vote nationwide wins the presidency, with roughly a third (35 percent) preferring to keep the Electoral College. That's essentially "almost two-thirds" accurate. Pew Research Center
Gallup's most recent update (fall 2025) found similarly, with 58 percent favoring amending the Constitution to elect presidents by popular vote versus 39 percent preferring the current system. Gallup
An Economist/YouGov poll from earlier this summer landed lower 56 percent would approve of an amendment abolishing the Electoral College, with 23 percent opposed and 21 percent unsure. Truthout
So "close to two-thirds" is the high end of a range that runs roughly 56–63 percent depending on pollster and year, with Pew's 63% being the number most likely behind the claim.
The partisan split — this is where "across both parties" gets complicated
It's true majorities of both parties lean toward the popular-vote option, but the gap is enormous, not marginal: 80% of Democrats favor moving to a popular vote system, versus 46 percent of Republicans. Gallup's numbers show an even wider gap 82 percent of Democrats versus 32 percent of Republicans. So it's fair to say Republicans are closer to an even split than a majority in some readings, and "across both parties" undersells how lopsided this is by party. Pew Research CenterGallup
On the Constitution point
That part is accurate and important: a Supreme Court ruling and existing constitutional structure strongly suggest a change of this kind would require a constitutional amendment and amending the Constitution requires two-thirds of both houses of Congress plus three-quarters of state legislatures, a bar polling majorities alone don't come close to clearing. That's also why the National Popular Vote Interstate Compact exists as a workaround an interstate agreement to award electors to the national popular-vote winner without touching the Constitution at all. Pew Research Center
Bottom line "Almost two-thirds" is a fair characterization of the strongest recent number (Pew's 63 percent), the constitutional-amendment framing is accurate, but "across both parties" is doing some quiet work it's majority support in both parties by some measures, but a 30-40 point gap, not a bipartisan consensus.