President Biden is struggling to overcome doubts about his leadership inside his own party and broad dissatisfaction over the nation’s direction, leaving him trailing behind Donald J. Trump just as their general-election contest is about to begin, a new poll by The New York Times and Siena College has found.

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…


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