Warren’s liberalism, meanwhile, did make some voters anxious, exit polls showed. But most swing voters do not follow the minutiae of policy debates, and many simply decided that she understood their problems better than Trump.

She and Holder consciously borrowed from the populist strategy of Obama’s 2012 campaign against Mitt Romney. Rather than emphasize Trump’s personal behavior, as the 2016 Clinton campaign did, they cast him as a greedy billionaire who corruptly used the presidency to enrich himself further. They also largely ignored Trump’s repeated criticisms of the ongoing N.F.L. national anthem protests.

The Democrats paired their message with broadly popular economic proposals: tax increases on the rich, expanded Medicare and child care, free community college and — highlighting an unfulfilled Trump promise — an infrastructure program. Budget watchdogs said the Warren agenda would increase the deficit. Many voters, evidently, did not care.