Donald J. Trump’s lead in the 2024 presidential race has widened after President Biden’s fumbling debate performance last week, as concerns that Mr. Biden is too old to govern effectively rose to new heights among Democrats and independent voters, a new poll from The New York Times and Siena College showed.

Mr. Trump now leads Mr. Biden 49 percent to 43 percent among likely voters nationally, a three-point swing toward the Republican from just a week earlier, before the debate. It is the largest lead Mr. Trump has recorded in a Times/Siena poll since 2015. Mr. Trump leads by even more among registered voters, 49 percent to 41 percent.

Doubts about Mr. Biden’s age and acuity are widespread and growing. A majority of every demographic, geographic and ideological group in the poll — including Black voters and those who said they will still be voting for him — believe Mr. Biden, 81, is too old to be effective.

Overall, 74 percent of voters view him as too old for the job, up five percentage points since the debate. Concerns about Mr. Biden’s age have spiked eight percentage points among Democrats in the week since the debate, to 59 percent. The share of independent voters who said they felt that way rose to 79 percent, nearly matching the Republican view of the president.

The poll offers early empirical evidence of what many Democrats have feared: That Mr. Biden’s faltering debate performance has further imperiled his chances against Mr. Trump this fall. Some Democratic lawmakers and donors are raising questions about Mr. Biden’s fitness following his struggles to finish his thoughts or articulate a vision during the debate, and they are demanding that Mr. Biden prove for a skeptical public that he is capable of serving until he is 86.