Aides said later that Mr. Obama might have been referring more to the limit on presidential tenure, and his view that George Washington set the right precedent by leaving after two terms. But his words could certainly be extended to Congress.

Proponents of term limits say Mr. Trump’s position has put new energy behind the campaign to adopt a constitutional amendment restricting House members to three two-year terms and senators to two six-year terms.

“The other part of the pressure is going to come from the public,” said Nick Tomboulides, the executive director of the group U.S. Term Limits. “When they know term limits is an issue on the table, they will make it very difficult for Congress to ignore. I think Congress is going to be forced to vote on it.”

Term limits have always been popular with voters and got a surge of momentum in the “throw the bums out” political atmosphere of the early 1990s, leading multiple states to adopt them for their legislatures through ballot initiatives and other means.

As part of the “Contract With America” in 1994, Republicans led by Representative Newt Gingrich of Georgia promised the “Citizen Legislature Act” and a “first-ever vote on term limits to replace career politicians with citizen legislators.” The mantra helped them topple Speaker Thomas S. Foley of Washington, a staunch opponent of term limits, via a challenger, George Nethercutt, who promised to serve just six years (though he later violated that pledge).

That term limits vote did come in March 1995 and won a majority but fell more than 60 votes short of the two-thirds majority necessary to advance a constitutional amendment. Forty Republicans, many of them committee and subcommittee chairmen, joined Democratic opponents in defeating the proposal. The amendment again fell short a year later.

Opponents argued then, and argue now, that arbitrary term limits would rob Congress of the institutional knowledge and expertise needed to conduct business and that voters had regular opportunities to end the service of their lawmakers. They don’t talk about how gerrymandering and the advantages of incumbency make it hard to defeat sitting lawmakers.