An overwhelming majority of Republican voters say their party’s leaders should get behind Donald J. Trump, even as he enters the general election saddled with toxic favorability ratings among the broader electorate, according to the latest New York Times/CBS News poll.

And as Mr. Trump faces deep skepticism with general election voters and some Republican holdouts, the Democratic front-runner, Hillary Clinton, is grappling with Senator Bernie Sanders and how to win over his impassioned supporters.

Both parties thus approach their July nominating conventions with significant unease and hurdles to overcome. Mr. Trump and Mrs. Clinton are widely disliked by voters, and both parties will need to repair schisms that might spell doom in an ordinary election year. But this, of course, is no ordinary year.

Mr. Trump’s and Mrs. Clinton’s soaring levels of unpopularity are extraordinary for the likely nominees of the two major parties. Nearly two-thirds of voters, for example, say that Mr. Trump is not honest and trustworthy. Just as many say the same of Mrs. Clinton. Strong majorities of voters say the candidates do not share their values.