For Hillary Clinton, Britain’s emotionally charged uprising against the European Union is the sort of populist victory over establishment politics that she fears in the coming presidential election.

Mrs. Clinton shares more with the defeated “Remain” campaign than a similar slogan — her “Stronger Together” echoing its “Stronger In.” Her fundamental argument, much akin to Prime Minister David Cameron’s against British withdrawal from the European Union, is that Americans should value stability and incremental change over the risks entailed in radical change and the possibility of chaos if Donald J. Trump wins the presidency.

She offers reasonableness instead of resentment, urging voters to see the big picture and promising to manage economic and immigration upheaval, just as Mr. Cameron did. She, too, is a pragmatic internationalist battling against nationalist anger, cautioning that the turmoil after the so-called Brexit vote underscores a need for “calm, steady, experienced leadership in the White House.”

But prudence is cold comfort to people fed up with more-of-the-same.

According to their friends and advisers, Mrs. Clinton and former President Bill Clinton have worried for months that she was out of sync with the mood of the electorate, and that her politically safe messages — like “I’m a progressive who gets results” — were far less compelling to frustrated voters than the “political revolution” of Senator Bernie Sanders or Mr. Trump’s grievance-driven promise to “Make America Great Again.”