Biden Facing Challenges in Two Must-Win States, Times/Siena Polls Find

President Biden is locked in a tight race with former President Donald J. Trump in Pennsylvania, a state that Mr. Biden barely won in 2020 and that is critical to his re-election hopes, and in Virginia, a state where Mr. Biden defeated Mr. Trump by 10 percentage points in 2020, according to the latest New York Times/Siena College polls.

The polls, which were completed before the assassination attempt on Mr. Trump while he was campaigning in Pennsylvania on Saturday, found that Mr. Trump was leading the president by 48 percent to 45 percent among likely voters in Pennsylvania. The results are almost unchanged from a New York Times/Siena College poll taken in May and within the margin of error.

By almost any Electoral College map calculation, it would be nearly impossible for Mr. Biden to win re-election without Pennsylvania.

Of potential greater concern for Mr. Biden and Democrats in the polls, which were conducted from July 9 through July 12, is the prospect that Virginia, a state that few strategists from either party thought would be in contention this year, appears to have turned competitive in a Trump-Biden rematch. In that state, Mr. Biden has a lead of 3 percentage points over Mr. Trump among likely voters, which is within the margin of error.

The last time a Republican won Virginia in a presidential race was 2004, when President George W. Bush beat his Democratic challenger, John F. Kerry, on his way to winning a second term in the White House.

“Joe Biden doesn’t really stand for traditional American values,” said Kendall Wood, 31, a truck driver who is an independent voter from Richmond, Va. He voted for Mr. Biden in 2020 and said he would support Mr. Trump — if he voted at all — this year. “Trump is more appealing to me simply because, again, I feel like his policies would empower me as opposed to hinder me,” he said.