Ken Paxton, the firebrand Texas attorney general, said last year that he thought he would need about $20 million to unseat Senator John Cornyn.

So far, Mr. Paxton is far short of his mark.

Many of the wealthy donors who bankrolled his political career in Texas have decided to watch from the sidelines during the U.S. Senate race, according to an analysis of state and federal campaign finance data by The New York Times.

Several businessmen who spent millions on Mr. Paxton’s campaigns for state attorney general have not given to either his Senate campaign or a political action committee backing his run, including a former top donor who gave far more to Mr. Cornyn.

Perhaps most strikingly, the billionaire West Texas oilmen and far-right kingmakers who have long supported Mr. Paxton have spent little on his Senate run.

Mr. Paxton’s fund-raising struggles underscore the deep rift in the Republican Party between its more business-oriented conservatives, who prefer Mr. Cornyn, and the hard-right base that embraces Mr. Paxton’s pugnacious politics.

His strong position in the race, despite a large fund-raising disadvantage, also reveals the limits of campaign spending in an election where the candidates are so well-known to voters, and where each has used his office to garner headlines for free. The runoff is May 26.

Recent polls have shown Mr. Paxton with a lead or neck-and-neck with Mr. Cornyn. But Democrats, who see Mr. Paxton as a weaker candidate in a general election, may find that if he becomes the nominee, conservative campaign money will come rushing his way.

One prominent Texas donor, Alex Fairly, said what was most important to him was beating the Democratic nominee, James Talarico — not who wins the primary.

“It’s more a matter of saving my bullets for the general,” Mr. Fairly, an Amarillo businessman, said in an interview. “Winning in November is more important.”

Mr. Fairly gave $7,000 to Mr. Paxton’s Senate campaign — far less than the $300,000 he has contributed to Mr. Paxton’s state campaigns since 2021.

In the race so far, Mr. Cornyn has significantly outspent Mr. Paxton, and still had $11 million in his campaign and committee accounts as of the latest filling — three times as much as Mr. Paxton had on hand. In total, Mr. Paxton has raised only around $13.5 million between his campaign and the committee supporting him.

Mr. Paxton’s campaign declined to comment. But on the campaign trail, he has presented his fund-raising gap as a strength.

“I was outspent $100 million to $5 million,” Mr. Paxton recently told a gathering of far-right activists. “I can tell you this: Most of his money did not come from people like you.”

Mr. Paxton has raised more than $1 million in contributions of $200 or less, while Mr. Cornyn has taken in around $300,000 in such contributions.

Compared with other Texas Republicans, such as Mr. Cornyn and Gov. Greg Abbott, Mr. Paxton, who has fought to overcome past scandals, has not been as strong a fund-raiser.

And some of his wealthiest backers, including well-known Texas businessmen who supported his last re-election campaign in 2022, have slipped away. So far a vast majority of his very top donors have contributed less, if at all, to his Senate run, the analysis showed.

The most conspicuous absentees have been the West Texas oilmen: Tim Dunn, and the brothers Farris and Dan Wilks. Over the last five years, Mr. Dunn and the Wilks brothers have given Mr. Paxton more than $1 million directly or through political action committees they direct.

But only Dan Wilks has contributed to Mr. Paxton’s run for U.S. Senate, throwing $7,000 to his campaign. Mr. Dunn has spent millions in other federal races.

Other past donors who have been sitting the race out include Jerry Jones of the Dallas Cowboys and Don Wasek, who founded Buc-ee’s, a beloved Texas gas station chain.

Michael Porter, a rancher and another major Paxton donor, gave $7,000 to Mr. Paxton’s campaign — the federal limit — and nothing to Paxton’s political action committee, which has no such limits. Then in November, Mr. Porter donated $50,000 to the committee supporting Mr. Cornyn.

At the same time, Mr. Paxton has also attracted new donors, including some who have given more than $250,000 each.

Matt Mackowiak, a senior adviser to Mr. Cornyn, said Mr. Paxton had made a lot of “macho pronouncements” but had failed to follow through. He said Mr. Cornyn was the only candidate with the funds to go up against Mr. Talarico.

Republican political consultants said the primary has placed donors in a difficult position.

President Trump has not endorsed in the race, and backing the loser could put donors on the outs with the eventual senator from Texas. The easier choice, the consultants said, is to wait and throw everything at Mr. Talarico.

Brendan Steinhauser, who worked on Mr. Cornyn’s 2014 campaign, said donors may also think Mr. Paxton can win without their cash. Mr. Cornyn finished first in the primary, but only by about a point and a half.

“Money per vote, obviously Paxton comes in way ahead,” Mr. Steinhauser said.