While not predictive, recent surveys provide a foundational baseline at the start of a race potentially between two universally known figures, foreshadowing a campaign without a clear front-runner. Polls by Yahoo News, The Wall Street Journal and Morning Consult have found the president slightly ahead while surveys by The Economist and the Harvard University Center for American Political Studies found him tied or trailing by several points. Mr. Biden faces similarly mixed results against Gov. Ron DeSantis of Florida, the strongest challenger to Mr. Trump for the Republican nomination.

The results point to a calcification in American politics where the leaders of both parties have a similarly sized core of support among voters not open to the other side regardless of developments in the news. The days when presidents could enjoy approval ratings above 50 percent or double-digit leads over challengers for any sustained period of time appear to be long over. And so if widespread support is no longer achievable, the challenge for Mr. Biden is to reassemble the coalition that provided him a 4.5-percentage-point victory nearly three years ago.

Mr. Biden has dismissed the importance of polls, saying that he is no different from other presidents at this point in their terms. “Every major one who won re-election, their polling numbers were where mine are now,” he told Stephanie Ruhle on “The 11th Hour” on MSNBC on Friday.

But in fact, only two of the past 13 presidents had approval ratings lower than Mr. Biden has at this point, according to an aggregate compilation by FiveThirtyEight.com — Mr. Trump and Jimmy Carter, both of whom lost re-election. More encouraging for Mr. Biden is the example of Ronald Reagan, who was just one-tenth of a point above where the current president is at this stage of his presidency, but came back to win a landslide re-election in 1984.