President Biden is trailing Donald J. Trump in five of the six most important battleground states one year before the 2024 election, suffering from enormous doubts about his age and deep dissatisfaction over his handling of the economy and a host of other issues, new polls by The New York Times and Siena College have found.

The results show Mr. Biden losing to Mr. Trump, his likeliest Republican rival, by margins of three to 10 percentage points among registered voters in Arizona, Georgia, Michigan, Nevada and Pennsylvania. Mr. Biden is ahead only in Wisconsin, by two percentage points, the poll found.

Across the six battlegrounds — all of which Mr. Biden carried in 2020 — the president trails by an average of 48 to 44 percent.

Discontent pulsates throughout the Times/Siena poll, with a majority of voters saying Mr. Biden’s policies have personally hurt them. The survey also reveals the extent to which the multiracial and multigenerational coalition that elected Mr. Biden is fraying. Demographic groups that backed Mr. Biden by landslide margins in 2020 are now far more closely contested, as two-thirds of the electorate sees the country moving in the wrong direction.

Voters under 30 favor Mr. Biden by only a single percentage point, his lead among Hispanic voters is down to single digits and his advantage in urban areas is half of Mr. Trump’s edge in rural regions. And while women still favored Mr. Biden, men preferred Mr. Trump by twice as large a margin, reversing the gender advantage that had fueled so many Democratic gains in recent years.