In all three states, Democratic Senate candidates were leading Republican incumbents by five percentage points or more. Senator Susan Collins of Maine, a Republican seeking a fifth term, is in a difficult battle against Sara Gideon, trailing by five points as voters there delivered a damning verdict on Mr. Trump’s stewardship: By a 25-point margin, 60 percent to 35 percent, they said they trusted Mr. Biden over Mr. Trump on the issue of the pandemic.

The poll, conducted among likely voters, suggests that the most endangered Republican lawmakers have not managed to convince many voters to view them in more favorable terms than the leader of their party, who remains in political peril with less than 50 days remaining in the campaign. Democrats appear well positioned to gain several Senate seats, and most voters say they would prefer to see the White House and Senate controlled by the same party. But it is not yet clear that Democrats are on track to gain a clear majority, and their hopes outside the races tested in the poll largely depend on winning in states Mr. Trump is likely to carry.