Responding to Tuesday’s results like an alarm bell in the night, Democrats on the ballot next year said that unless Mr. Biden and other party leaders addressed voters’ close-to-home frustrations, they were certain to lose their congressional majorities.

“We were so willing to take seriously a global pandemic, but we’re not willing to say, ‘Yeah, inflation is a problem, and supply chain is a problem, and we don’t have enough workers in our work force,’” said Representative Abigail Spanberger, a Virginia Democrat facing a bruising re-election. “We gloss over that and only like to admit to problems in spaces we dominate.”

More pointedly, Ms. Spanberger said Mr. Biden must not forget that, for many voters, his mandate was quite limited: to remove former President Donald J. Trump from their television screens and to make American life ordinary again.

“Nobody elected him to be F.D.R., they elected him to be normal and stop the chaos,” she said, alluding to the sweeping agenda the president is seeking to enact with the thinnest of legislative majorities.