SILSBEE, Tex. — The last time a Democrat won Texas in a presidential election was 1976, when voters chose Jimmy Carter over Gerald R. Ford. Carey Georgas was 22 back then, a disillusioned Democrat who voted for Eugene McCarthy, the independent candidate, and who was working at Cravens Insurance in this East Texas town.
Forty years later, Mr. Georgas, 62, is still a Democrat, but not so disillusioned. He says he is voting for Hillary Clinton and has been following the polls showing Donald J. Trump with a narrow lead over her in Texas, one so slim that it fell within the margin of error in some surveys.
Yet, like many Democrats in a state that has voted to send Republicans to the White House in nine consecutive presidential races spanning four decades, he is equal parts optimist, realist and pessimist. Many of his friends and neighbors are Republicans who are supporting Mr. Trump.
“I’m bumfuzzled by the whole thing,” said Mr. Georgas, now the president of Cravens. “I don’t think she’ll win the state. But I think she’ll close the margin closer than anybody has.”
It is a question being asked by Democrats and Republicans alike: Can Mrs. Clinton win Texas? Democrats in the state call it a long shot, but some say they believe she has a chance; Republicans say it will be close but are confident that Mr. Trump will triumph. Political consultants who have both Republican and Democratic clients, and people who study Texas politics, say regardless of Mr. Trump’s narrow lead, he will take the state.
“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.”
Lionel Sosa, 77, a Republican media consultant in San Antonio who created ads for Ronald Reagan and other Republicans, said he would vote for Mrs. Clinton, calling it a “protest vote.”
State Representative Richard Peña Raymond, a Laredo Democrat who is the Texas political director for the Clinton campaign, said that as Mr. Trump has angered women, Mexican-Americans and moderate Republicans, he has helped Mrs. Clinton gain support.
“The longer this campaign keeps going, the less support Trump has in Texas and the more support Hillary has in Texas,” he said. “Each day is a good day for Hillary and it almost appears like each day is a bad day for Trump. I don’t think it’s specific to Texas.”
Republicans equate the Democratic enthusiasm with Wendy Davis’s much-hyped but unsuccessful bid to become governor, and they accuse Democrats of creating a false perception that Mrs. Clinton can win Texas to raise money for down-ballot races. Texas Democrats have not won a governor’s race since 1990 and have not won even one statewide elected office since 1994.
There is widespread disenchantment with Mr. Trump among Texas Republicans, but Mrs. Clinton remains unpopular in parts of the state. She is seen as an establishment politician and regarded as an anti-gun abortion rights supporter in an anti-establishment, anti-abortion and pro-gun state. And she is tied to President Obama, who lost Texas in 2012 by nearly 1.3 million votes.
Some Texas Republicans, dissatisfied with both Mr. Trump and Mrs. Clinton, said they would go to the polls on Election Day but not vote for anyone for president.
“I really am in a quandary,” said John Andrade, 45, a Hispanic Republican who owns a marketing and advertising company in San Antonio. “I don’t know if I’ll leave that top blank or not.”
But others, even those who had concerns over Mr. Trump’s comments about groping women and who supported Senator Ted Cruz or other candidates in the primary, said they would vote for Mr. Trump regardless.
“Everybody has problems with those comments, but they have a bigger problem with what Hillary has said, done and will do if elected president of the United States,” said Jared Woodfill, an evangelical Christian who is a former chairman of the Harris County Republican Party in Houston and who is supporting Mr. Trump.
In Silsbee, a working-class town of 6,700 in a wooded region known as the Big Thicket, Mr. Georgas and his support for Mrs. Clinton is uncommon. Hardin County, which includes Silsbee, is dominated by Republicans, but its Democratic past was not so long ago. As recently as 2004 and 2008, Hardin County voters were electing some Democrats for local offices, while supporting Republicans for president. Many of the older Republicans in Hardin County spent much of their lives as Democrats — including voting for Mr. Carter in 1976 — but they switched parties in the past several elections as the state tilted right.
“This was not a Trump county during the primary,” said Kent Batman, who is the chairman of the county Republican Party and who voted for Mr. Cruz in March. “But we’re 100 percent Trump now. And it’s because we absolutely can’t stand Hillary Clinton.”
Janis Holt, 56, who is the president of the Hardin County Republican Women and owns an air-quality systems company with her husband, voted for Senator Marco Rubio in the primary. Mr. Trump will get her vote in November.
“He was not my first choice,” she said. “This is not about a person. It’s about a platform and an ideology. Mr. Trump will earn my vote because he represents my party. His personal life doesn’t represent me at all.”