Nearly two in three Americans say they think Mr. Trump is unqualified to be president and are anxious about the idea of him in the White House, the Post-ABC poll found. In contrast, 61 percent think Mrs. Clinton is qualified.

Mr. Trump is coming off two particularly damaging weeks for his campaign — a period in which he personally attacked a Mexican-American judge hearing a lawsuit against Trump University, gloated about predicting attacks like the Orlando massacre that left 49 dead, and fired his embattled campaign manager.

Despite his woes, not all the results of the new polls were heartening for Mrs. Clinton. The Journal-NBC survey found that her lead essentially disappears when candidates from the Green Party and Libertarian Party are included. She essentially tied Mr. Trump, with 39 percent to his 38 percent. Together, third-party candidates grabbed 16 percent of the support.

Senior aides to both candidates spoke on Sunday morning news shows, and their words left little doubt about the intensity that the race is taking on now that the nominating fights have ended.

Robby Mook, Mrs. Clinton’s campaign manager, said on Fox News Sunday, “Donald Trump is probably one of the most reckless, unfit candidates to ever seek the presidency.” Mrs. Clinton, he said, is “probably one of the most prepared.”