With eight months left until the November election, Mr. Biden’s 43 percent support lags behind Mr. Trump’s 48 percent in the national survey of registered voters.

Only one in four voters think the country is moving in the right direction. More than twice as many voters believe Mr. Biden’s policies have personally hurt them as believe his policies have helped them. A majority of voters think the economy is in poor condition. And the share of voters who strongly disapprove of Mr. Biden’s handling of his job has reached 47 percent, higher than in Times/Siena polls at any point in his presidency.

The poll offers an array of warning signs for the president about weaknesses within the Democratic coalition, including among women, Black and Latino voters. So far, it is Mr. Trump who has better unified his party, even amid an ongoing primary contest.