Democratic presidential hopeful Joseph R. Biden leads President Trump in the Republican bastion of Texas, according to a new Quinnipiac University poll released Wednesday.

Mr. Trump does beat other major Democratic candidates including home-state former Rep. Beto O’Rourke and former San Antonio Mayor Julian Castro, but in each case, the margin is so small that it is likely to be of little comfort to Republicans.

Quinnipiac says Mr. Trump leads Sen. Elizabeth Warren 46% to 45%, and leads Sen. Bernard Sanders 47% to 44%.

Mr. Biden, though, tops Mr. Trump 48% to 44%.

The pollsters said that’s in “too-close-to-call” territory, which is bad news for a Republican, particularly a sitting president. Texas is usually the biggest GOP-gimme on the map, and losing it — or even having to spend money defending it — could be a major dent to Republicans’ chances next year.

Mr. Trump’s approval rating in the state is split at 48% approval and 49% disapproval — even though voters told the pollsters that they are generally better off financially now than they were in 2016.

Texas voters also are skeptical of impeachment, with 60 percent saying they don’t want to see Congress go down that route.

Quinnipiac found that Texas voters would prefer Mr. O’Rourke forgo the race and instead run for Senate against Sen. John Cornyn. Mr. O’Rourke narrowly lost a race last year against the other Republican senator, Ted Cruz.

Quinnipiac surveyed 1,159 voters from May 29 to June 4. The poll had a margin of error of plus or minus 3.4 percentage points.

Mr. Trump has seen scare polls out of Texas before.

A Washington Post poll released in September 2016 showed Democratic candidate Hillary Clinton with a 1% lead over Mr. Trump, and a YouGov survey a month later, just two weeks before the election, stil put Mrs. Clinton within 3 percentage points of Mr. Trump.

He would end up winning the state by 9%.

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