Biden holds a steady lead in Nevada, which Trump hopes to flip, Times/Siena poll shows.

Joseph R. Biden Jr. has a steady lead over President Trump in Nevada, a state that has been shading blue in recent elections but that Mr. Trump is hoping to flip, according to a New York Times/Siena College poll released on Tuesday.

Mr. Biden, the Democratic nominee, leads Mr. Trump 49 percent to 43 percent among likely voters in Nevada, with 4 percent undecided or declining to state a preference. The poll was taken after the presidential debate last week, one of Mr. Trump’s last opportunities to change the trajectory of the race.

The results are virtually unchanged from another Times/Siena poll in the state conducted this month after Mr. Trump announced he had tested positive for the coronavirus, which found Mr. Biden leading Mr. Trump 48 percent to 42 percent among likely voters.

With just a week until Election Day and little time for Mr. Trump to make up any ground, the results underscore the challenges he faces in diverse battleground states that once seemed attainable, if not downright winnable, for an incumbent Republican president. Polls have also shown Mr. Trump trailing Mr. Biden in neighboring Arizona, a state that has not voted for a Democrat for president since 1996.

Mr. Trump has continued to fight for Nevada, visiting the state twice since securing the Republican nomination for re-election; on Wednesday, he is planning to hold a rally just across the border in Bullhead City, Ariz. In September, The Cook Political Report shifted its assessment of the Nevada race in Mr. Trump’s direction, from “likely Democrat” to “lean Democrat.”

But Mr. Biden’s polling lead underscores the shifting dynamics of a consummate swing state that has taken on a Democratic tilt. Hillary Clinton won the state in 2016 by just over two percentage points, 10 points less than Barack Obama’s margin of victory in 2008. But in 2018, the state elected Senator Jacky Rosen, a Democrat, who ousted the Republican incumbent Dean Heller; and Gov. Steve Sisolak, the first Democrat to lead the state since 1999.

Mr. Biden is being buoyed by Hispanic voters, young voters and women, and trailing Mr. Trump among white voters without college degrees, the survey showed. Among Hispanic voters, who make up about 20 percent of eligible voters in the state, Mr. Biden held a commanding lead over Mr. Trump, 59 percent to 30 percent.