“This year, it appears anything is possible, but a Clinton victory in Texas remains extremely unlikely,” said Mark P. Jones, a political science fellow at the Baker Institute of Rice University in Houston.

But some Democrats, pointing to the recent polls, see it differently. They predict a large turnout by black and Latino voters. And they have become energized as the Clinton campaign has opened offices and run TV ads in Texas and as local Republican-to-Democrat defections have made the news. Lauren Parish, a Republican judge in East Texas, said on Friday that she was leaving the party and becoming a Democrat because she saw “no way of reconciling my Christian beliefs with the manner in which the Republican Party is conducting itself.”

Gilberto Hinojosa, the chairman of the Texas Democratic Party, said of Mrs. Clinton, “I think she can carry Texas.”

“We’re looking at this cleareyed, but we have never been this close in a presidential election, at least for many years,” he said. “This election may be different because Republicans irresponsibly nominated someone who is just so far out there in every aspect.”