Steve Snyder, a college professor from Des Moines, expressed respect for Mr. Biden as he waited for Mayor Pete Buttigieg of South Bend, Ind., to address a shivering crowd gathered outside a Des Moines high school on Saturday night . But, noting the pace of the president’s broadsides against Mr. Biden, he said that the Biden campaign appeared to be “slow-footing” their response, even as he acknowledged the challenges of responding to Mr. Trump.

“This isn’t a typical campaign,” said Mr. Snyder, who said he is leaning toward supporting Ms. Warren. “This is information warfare. They’re just not responding quick enough.”

Asked to address concerns that Mr. Biden’s message was getting drowned out, a view which was shared by some other Iowa voters, Mr. Biden’s campaign spokesman, T.J. Ducklo, said in a statement Sunday that Mr. Biden “will continue punching back hard against Donald Trump’s pathetic and increasingly unhinged behavior, while also keeping the focus on issues where Trump has failed middle class families, like rising health care costs and the urgent climate crisis.”

He also cited Mr. Biden’s standing in recent polls, arguing that “these attacks aren’t working with Democratic voters.” Mr. Biden’s numbers have generally remained steady at the national level since the controversy over Ukraine broke open last month.

Yet Mr. Biden, who months ago held a commanding edge over his rivals, has nearly lost his lead in primary polls, having dipped well below 30 percent in The New York Times national polling average. He is barely ahead of Ms. Warren in that ranking, which gauges national support, and he is tied with her, or trailing, in three of the four early-voting states. While Mr. Biden maintains a powerful bloc of support in the race, built on the loyalty of African-American voters and moderate whites, that coalition has been shrinking rather than growing — a trend he must reverse if he is to become the nominee.

Mr. Biden raised $15.2 million in the third quarter, a sturdy sum but far less than what Mr. Sanders and Ms. Warren collected. He also trails Mr. Buttigieg, who has become a cause célèbre for many party donors.