White House officials on Sunday shrugged off weekend polling that showed President Biden trailing former President Donald J. Trump, even as Democrats said they were increasingly worried about Mr. Biden’s chances in 2024.

The new polling from The New York Times and Siena College found Mr. Biden losing in one-on-one matchups with former President Donald J. Trump in five critical swing states: Arizona, Georgia, Michigan, Nevada and Pennsylvania. Mr. Biden is ahead by two percentage points in Wisconsin.

Although the polling is worrisome for the president, Mr. Biden still has a year to campaign, which his team emphasized on Sunday. They noted that polls have historically failed to predict the results of elections when taken a year ahead of time.

“Gallup predicted an eight-point loss for President Obama only for him to win handily a year later,” said Kevin Munoz, a spokesman for Mr. Biden’s campaign. “We’ll win in 2024 by putting our heads down and doing the work, not by fretting about a poll.”

Still, the results of the poll, and other recent surveys showing similar results, are prompting public declarations of doubts by Democrats.

David Axelrod, a Democratic strategist who has expressed concerns about Mr. Biden before, wrote on X, formerly known as Twitter, that the new polling “will send tremors of doubt” through the party.