AUSTIN — Texas Republicans are on edge as polls show President Trump and presumptive Democratic nominee Joe Biden running neck and neck in the Lone Star State with less than five months to go before Election Day.

Most GOP operatives in the state still view Trump as the odds-on favorite to carry Texas and its 38 Electoral College votes in November. But they’re increasingly open to the outside possibility that Texas could go blue in the presidential race for the first time since 1976.

The president’s margins in Texas will matter, and Republicans fear that a close race at the top of the ticket might wipe them out in down ballot races.

Five House Republicans from the Texas delegation are retiring at the end of the year and the nonpartisan Cook Political Report rates three of those as either toss-ups or leaning Democratic.

Sen. John Cornyn (R-Texas) is also up for reelection and will likely face the toughest fight of his career in 2020.

Biden’s campaign says it intends to compete in Texas, where the state Democratic Party has become one of the largest in the nation. Texas’s fast-changing demographics have hastened its move from solidly red state to purple battleground.

“It is a very serious moment for Republicans in Texas,” said Bill Miller, a veteran Republican campaign operative in Austin. “Any Republican that doesn’t take the moment seriously will be surprised in a very bad way in November. They have to be alert and engaged or they’ll find themselves in trouble with a capital T.”

A Quinnipiac University survey released last week found Trump leading Biden by 1 point in Texas. Trump leads by 2.2 points in the RealClearPolitics average.

Texas Republicans are primarily worried about their standing in the suburbs, where women and independents have steadily gravitated away from the GOP since Trump took office.

Republican support has eroded in the areas surrounding Houston, Dallas, Austin and San Antonio, four of the nation’s largest and fastest growing metro areas. Democrats defeated longtime GOP incumbents in Houston and Dallas in 2018.

Republicans say Trump has so far missed an opportunity to appeal to suburban voters in Texas during this time of historic civil unrest around the police killing of George Floyd.

“The suburbs are a concern because any time your stronghold is showing weakness, it needs to be shored up,” said Corbin Casteel, a veteran GOP operative based in Austin.

“The president would help to show compassion in times like this. Texas Republicans are largely Christians, they love Jesus and live their lives in that way and it’s disappointing to see the leader of our party do such a great job on the economy and jobs and in appointing conservative justices, but to miss these opportunities to lead with that kind of compassion. If he had been leading in that way throughout this racial crisis, I think his numbers would be through the roof. It doesn’t mean he’ll lose Texas, I definitely don’t think he will. But it’s a missed opportunity to shore up a stronghold.”

Casteel, who led the Trump campaign’s operations in Texas for several months in 2016, said he expects Trump to win the state by about 6 points in 2020, which would be the closest contest in modern times.

Trump’s 9-point victory in Texas in 2016 was the closest presidential outcome since former President Jimmy Carter (D) carried the state more than 40 years ago. A Democrat has not won statewide in Texas since 1994, the longest streak in the nation.

Casteel warned that a smaller-than-expected victory for Trump could mean “devastation” for the GOP at the state level and in districts for state legislative seats.

Still, Casteel said that the GOP’s standing in the state may be underestimated amid the national focus on whether Texas is at a tipping point.

Republicans are excited about some of their House recruitment victories, including Genevieve Collins, the Dallas businesswoman who is taking on freshman Rep. Colin Allred (D-Texas) in Dallas.

Casteel expects Republicans to rally around Trump as the campaign heats up and Biden is forced into the spotlight.

“Texans really like Trump’s economic policies and they love his judicial appointments,” Casteel said. “When it comes down to walking into the voting booth and pulling the lever, I think it will be an easy decision.”

Brendan Steinhauser, an Austin-based GOP strategist, put the odds of Texas going blue in the presidential race at 33 percent.

He said he expects Cornyn to win reelection and to potentially outpace Trump by about 5 points. Cornyn will find out who his Democratic challenger is next month, when former Air Force pilot MJ Hegar and state Sen. Royce West square off in a runoff election.

Biden’s likeliest path to victory in Texas, Steinhauser said, would be for frustrated Republicans to stay home or to show up at the polls and leave the presidential line blank, while checking the mark for Cornyn and other GOP candidates down the ballot.

“I do think the state is in play and it’s going to be decided by a narrow margin,” Steinhauser said. “That said, I think Trump will win. Republicans are taking this election very seriously. We know it’s competitive. [Former Democratic Rep.] Beto O’Rourke won a lot of suburban white women in the 2018 Senate race and if Democrats hold on to those voters, it will be very close. But Republicans still outnumber Democrats in Texas, and if they turn out to vote for Trump, we should be OK.”

In the 2018 midterms, O’Rourke fell short to Sen. Ted Cruz (R-Texas) by 2.5 points. But O’Rourke turned out more voters in Texas than Democratic presidential nominee Hillary Clinton did in 2016.

Also in 2018, Democrats picked up two GOP-held House seats in Texas. Six other GOP House members in Texas won reelection by 5 points or fewer. The Democratic Congressional Campaign Committee has opened headquarters in Texas, making it the only state nationwide where the House campaign arm has a full team on the ground.

Democrats also picked up 12 state House seats and two state Senate seats in 2018. Republicans are down to a nine-seat advantage in the state House. Democrats say 22 state House seats are polling in single-digit territory and are up for grabs.

Texas has added more than 2.5 million people to its voter rolls since 2016. The state does not register voters by party, but many of the new voters are believed to be young people, Latinos, or newcomers from blue states, such as California, Illinois and New York.

“This was the state that helped create George W. Bush’s compassionate conservatism, the Tea Party and the Trump movement, and now all of that could change on a dime to become a new Democratic movement,” said Manny Garcia, executive director of the Texas Democratic Party. “Republicans got lazy and completely missed the wake-up call about the direction things have been headed here. The population growth has made Texas competitive at every level.”