They campaigned urgently, even frantically, at airfields and arenas, on a college campus in Wisconsin and in a Philadelphia church. Hillary Clinton and Senator Tim Kaine, their prospects brightened by news that the F.B.I. had found no new troublesome emails in a review of Mrs. Clinton’s private server, pleaded with Americans on Sunday to get out and vote as if their very way of life were on the line.

Scrambling across the electoral map, Donald J. Trump and his running mate, Gov. Mike Pence, addressed supporters in darker and even graver terms, with Mr. Trump casting the election as a now-or-never moment for his brand of right-wing nationalism.

Surpassing the anxious entreaties of an ordinary presidential race, Mrs. Clinton and Mr. Trump begged voters to see the 2016 election as a choice of almost apocalyptic significance. Mr. Trump called the vote on Tuesday a final chance to turn back foreign forces menacing American identity, while Mrs. Clinton said the country’s long journey toward equality for women and minorities was at risk of being reversed in a day’s balloting.