“I don’t think there’s ever been a moment like this one, a year like 2018,” Mr. O’Rourke said in an interview at the church. “People, myself included, want to be part of something greater than themselves, greater than a political party, greater than our differences. From the first time we came to Tyler a year and a half ago, to every visit since then, it’s been more of the same. That’s what leaves me encouraged.”

Both Mr. O’Rourke and Mr. Cruz campaigned in Tyler on the same day last week, holding rallies just a few miles and a few hours apart. Mr. O’Rourke drew about 1,000 to the church, while Mr. Cruz had more than 600 at a banquet hall.

On Oct. 18, The Longview News-Journal — the major paper in Longview, one of the largest cities in East Texas — endorsed Mr. O’Rourke, accusing Mr. Cruz of spending much of his time as the state’s junior senator on his failed bid for president in 2016.

The polls continue to underscore how unpredictable the race has become.

In the latest University of Texas/Texas Tribune Poll of likely voters, Mr. Cruz held a narrow lead of six percentage points over Mr. O’Rourke, with a margin of error of 3.22 percentage points. But the same poll showed other Texas Republicans with sizable leads over their Democratic opponents. Mr. Abbott had a 19-point advantage and Lt. Gov. Dan Patrick held an 18-point lead. That poll and others like it suggest that Mr. O’Rourke is running a stronger campaign than other Texas Democrats and that support for Mr. Cruz is softer than for other Republicans on the ballot.

“When a Democrat hasn’t won a Senate seat in Texas since 1988, you go into it knowing it’s always an uphill battle,” said State Representative Chris Turner, a Democrat who was the campaign manager during the final stretch of Ms. Davis’s run for governor in 2014. “But Beto I think is better positioned than any Democratic candidate has been in easily a generation.”

Republican strategists and Mr. Cruz’s supporters said they remain concerned about the tight race. Mr. O’Rourke has clearly won key campaign battles: He has raised more money than Mr. Cruz, and more of his signs and bumper stickers are visible throughout big-city and small-town Texas. But Republicans remain skeptical that he can win the overall war.

“I think that Texans are conservatives as a rule, and I don’t think they’ll vote for a guy that’s for more taxes and gun control and open borders,” said Kerry D. Pratt, a West Texas cotton farmer who is the chairman of the Republican Party in Floyd County, an agricultural community near Lubbock, where Mr. Cruz planned to campaign on Wednesday. “He’s getting the free press because he’s new. He’s handsome. But nobody believes what he believes around here.”