The giddy anticipation surrounding Democratic Rep. Beto O’Rourke’s bid for the Senate has sometimes obscured the fact Republicans dominate his state of Texas but reminders are beginning to surface.

A month ago, riding a surge of adulatory media and remarkable fundraising, Mr. O’Rourke appeared to be giving Republican Sen. Ted Cruz all the incumbent could handle in his re-election bid. Today, Mr. Cruz seems to have recaptured the momentum and has again taken a sizable lead in surveys, causing pollsters and political experts to say Mr. O’Rourke’s campaign has “hit a wall.”

The bricks in that wall, some experts argue, are made of Republican money.

Not Mr. Cruz’s money, to be sure. On that front, Mr. O’Rourke continues to shatter records, with his announced third quarter haul of more than $38 million the most any senatorial candidate has ever amassed in one quarter.

Instead, Mr. Cruz is benefiting from the other Republicans on the Texas ticket, most notably GOP Gov. Greg Abbott, who hold commanding leads in their races and therefore can spend their cash keeping the Lone Star State red.

“In the closing weeks of Texas campaigns there is an overwhelming advantage for Republican messaging, and that is funded by the tens of millions all the candidates have combined,” said Cal Jillson, a political science professor at Southern Methodist University in Dallas. “Because Abbott and (Lt. Gov. Dan) Patrick are not dealing with a formidable challenge to their re-election, they don’t have to spend all their money versus their opponent. And that tends to have a profound impact in the closing weeks on undecided and under-informed voters.”

Indeed, if Mr. O’Rourke’s campaign has plateaued, that’s not a coincidence, in Mr. Jillson’s opinion, it’s that Mr. Abbott dipped into his reported $50 million war chest and launched his first television advertising blitz two weeks ago.

Other states have a similar dynamic in which one statewide race could influence another. With much national attention focused on which party will control Congress come November, that answer could be influenced by matters off the national grid.

In Arizona, for example, where a pair of U.S. representatives are vying to replace outgoing Republican Sen. Jeff Flake, the governor’s race shadows the would-be senators.

Democratic Rep. Kyrsten Simena’s run against Republican Martha McSally there is a toss up complicated by a gubernatorial election that pits liberal Democrat David Garcia against incumbent Republican Doug Ducey, who currently leads Mr. Garcia by 15.7 percentage points in the RealClearPolitics average of polls.

Ms. Sinema, whose campaign was roiled last week by past reminders of her left-wing positions against the military and demeaning comments about Arizona and its voters, has labored to paint herself as a more moderate Democrat. She waited until Oct. 4 before revealing her opposition to Justice Brett M. Kavanaugh, and has also shied away from endorsing Mr. Garcia, leaving her as one of the only Arizona Democrats to remain neutral.

In Florida, too, the gubernatorial contest may have an impact on the senatorial one, although there the calculus helps Democrats.

With Republican Gov. Rick Scott term-limited out of Tallahassee, he is seeking to replace Democratic Sen. Bill Nelson in Washington. Mr. Scott has thus far held a fundraising edge over Mr. Nelson, but the race has remained neck-and-neck all year with neither candidate seemingly capable of maintaining a steady lead.

But where the Republican governors in Texas and Arizona offer help for the GOP senate candidate, the Democratic candidate to replace Mr. Scott as governor could help Mr. Nelson. That’s because the Democrat, Tallahassee Mayor Andrew Gillum, is a left-wing darling whose positions on many issues track those of socialist Sen. Bernard Sanders and have attracted the deep pockets of left-wing billionaires George Soros and Tom Steyer.

As a young black candidate who is now bankrolled by some of the Democratic Party’s top donors, Mr. Gillum could energize a base of millennial and minority voters who aren’t excited by Mr. Nelson’s candidacy and might otherwise stay home on Election Day, according to several Florida analysts.

“The reason for that thought is that it is the governor’s race that is mobilizing younger and minority voters, not the U.S. Senate race,” said Susan MacManus, a political science professor at the University of South Florida.

Of course, this is all what might be called reasonable speculation at this point, as Ms. MacManus acknowledged.

“The result will not be apparent until after the election when we get a good picture of the turnout patterns,” she said.

In Texas, Republicans are working hard to influence those patterns, and as with the cash, there is a symbiotic pattern to the work.

Mr. Abbott never fully dismantled his campaign apparatus when he won the governor’s election in 2014, and his re-election bid was able to plug right in to existing offices and staff. They have built what they call “Abbott U,” a training ground for Republican workers that are able to proselytize on behalf of the entire GOP ticket.

“This congressional election is a lot more competitive than usual and we have an excellent relationship with all our candidates,” said Dave Carney, the CEO of Norway Hill Associates who helped design “Abbott U.” The coursework is intense but short — basically a 4-hour seminar followed by four 45-minute video courses.

“It’s a way of creating what you might call ‘super volunteers,’” said John Wittman, press secretary for Mr. Abbott’s re-election campaign.

In a little over a year, this volunteer army has fanned out across Texas, following an algorithm that allows them to identify likely Republican voters and actually speak to them because “an actual conversation has seven times the value of someone seeing a television ad,” according to Mr. Carney’s calculus.

“The volunteers have talked to 2.1 million voters — not just door knocks, conversations,” Mr. Wittman said. “You can’t possibly talk to everybody but if we just wanted to deliver campaign literature we’d use the mail. We go to targeted doors.”

The O’Rourke campaign has a similar effort that involves Mr. O’Rourke crisscrossing the state and appearing in every county. But in the Lone Star State, the Republicans have a built-in advantage which, if tapped, should spell electoral success for GOP candidates for the senate, the governor’s mansion and beyond.

“The Democrats love to say they’d win elections if they could generate more turnout, but in reality there are more of our votes out there than theirs,” Mr. Carney said.