In the short run, Eisenhower was hurt; a summit meeting with the Soviet leader Nikita Khrushchev collapsed in acrimony. But the public eventually forgave him, Ms. Goodwin said, because he owned up to his mistake.

In 1974, at the height of the Watergate scandal, President Richard M. Nixon was accused of lying, obstructing justice and misusing the Internal Revenue Service, among other agencies, and resigned rather than face impeachment. Voters, accustomed to being able to trust politicians, were disgusted. In 1976, Jimmy Carter won the presidency after telling the public, “I’ll never lie to you.”

President Clinton was impeached for perjury and obstruction in trying to cover up his affair with an intern, Monica Lewinsky, during legal proceedings. Chris Lehane, a former Clinton adviser, said Mr. Clinton’s second-term agenda suffered during his impeachment, yet paradoxically his favorability ratings remained high — in part, Mr. Lehane said, because “the public distinguished between Clinton the private person and the public person.”

But sometimes it’s easier to tell what’s false than what’s a lie. President George W. Bush faced accusations that he and members of his administration took America to war in Iraq based on false intelligence about whether Saddam Hussein had weapons of mass destruction. Mr. Bush and his team emphasized and in some cases exaggerated elements of the intelligence that bolstered the case while disregarding dissenting information, leading critics to accuse them of lying. Among those who said Mr. Bush had lied was Mr. Trump.

Over the past two decades, institutional changes in American politics have made it easier for politicians to lie. The proliferation of television political talk shows and the rise of the internet have created a fragmented media environment. With no widely acknowledged media gatekeeper, politicians have an easier time distorting the truth.

And in an era of hyper-partisanship, where politicians often are trying to court voters at the extreme ends of the political spectrum, politicians often lie with impunity. Even the use of the word “lie” in politics has changed.

“There was a time not long ago when you could not use the word ‘lie’ in a campaign,” said Anita Dunn, once a communications director to Mr. Obama. “It was thought to be too harsh, and it would backfire. So you had to say they hadn’t been honest, or they didn’t tell the truth, or the facts show something else, and even that was seen as hot rhetoric.”