Hillary Clinton and Donald Trump Are Winning Votes.

Clinton during an event on Tuesday at the Palm Beach County Convention Center in Florida. 

The victories were lopsided. The celebrations were effusive. The delegates were piling up by the hundreds.

But Donald J. Trump and Hillary Clinton’s resounding triumphs on Tuesday masked a profound, historic and unusual reality: Most Americans still don’t like him. Or her.

Both major parties must now confront the depth of skepticism, resistance and distaste for their front-runners, a sentiment that would profoundly shape a potential general election showdown between Mr. Trump and Mrs. Clinton.

Even as they watched the two candidates amass large margins on Tuesday, historians and strategists struggled to recall a time when more than half the country has held such stubbornly low opinions of the leading figures in the Democratic and Republican Parties.

“There is no analogous election in the modern era where the two top candidates for the nomination are as divisive and weak,” said Steve Schmidt, a top campaign adviser to George W. Bush in 2004 and John McCain in 2008. “There is no precedent for it.”

Mrs. Clinton’s commanding wins in the swing states of Ohio, North Carolina and Florida seemed to hobble the once robust challenge of Senator Bernie Sanders. And Mr. Trump’s dominance in Florida, North Carolina and Illinois knocked out Senator Marco Rubio and propelled Mr. Trump even closer to the Republican nomination.

This would be the moment, under normal circumstances, when the de facto nominees, emerging victorious from the intramural skirmishes of their parties’ nominating contests, would invite an eager national electorate to take their measure. And in their victory speeches, both tried their best, issuing broad appeals for Americans to unite behind them.

But Mr. Trump has unnerved many Americans with his inflammatory oratory and radical-sounding proposals. And Mrs. Clinton, while viewed as a more seasoned and serious political figure, has struggled in her campaign to win the trust of the American electorate. And it is all but impossible for the country to take a fresh look at them.