Mr. Paxton is hoping to become the second Trump-endorsed challenger to oust a sitting senator this year, after Senator Bill Cassidy of Louisiana didn’t even make the runoff in his state earlier this month. Mr. Trump’s backing has proved formidable in the House, too, where he helped a G.O.P. challenger defeat Representative Thomas Massie of Kentucky last week.

The Senate race is the highest-profile contest on Tuesday, as Texas has emerged as a surprise addition to the map of competitive Senate races and the fight for the majority this fall. Mr. Cornyn and several of his Republican colleagues in the Senate decried the Paxton endorsement, arguing that Mr. Paxton is more vulnerable to an upset by James Talarico, a Democrat, than the incumbent is.

A number of intriguing and consequential runoffs are also appearing on the ballot. They include two representatives facing off against each other, one of whom will become the first Democratic incumbent to lose this year; and a border-district seat that pits a Democratic sex therapist accused of antisemitism who has been boosted by a secretive super PAC linked to Republicans against a sheriff’s deputy from Bexar County.

What else to watch on Tuesday:

Can Cornyn sell an electability pitch?

Mr. Cornyn has argued that Mr. Paxton would put the senior senator’s seat needlessly at risk this fall against Mr. Talarico in a state where Republicans haven’t lost statewide in three decades.

Mr. Talarico, a state legislator from Austin, has captured the attention of small Democratic donors who were drawn to his embrace of a religious message as a salve to the party’s generation-long struggles in the state. He raised $27 million in the first quarter, nearly four times what Mr. Paxton has raised in the entire race.

Mr. Trump’s endorsement last week of Mr. Paxton makes Mr. Cornyn the underdog: He rolled out a hashtag of “#stillwithCornyn,” which underscored the uphill nature of his re-election bid.

The race has broken primary advertising records, but Republicans warned that taking down Mr. Talarico could force the party to spend money in Texas in the general election.

A generational clash in Houston

No Democratic member of Congress has lost a primary so far in 2026, despite a groundswell of voter antipathy toward party leadership and the old guard.

That will change on Tuesday, when two incumbents will seek the same Houston-area seat in a test of the appetite of voters for generational change.

The race for the state’s 18th Congressional District pits Representative Christian Menefee, 38, against Representative Al Green, a 78-year old, 11-term incumbent. Mr. Menefee is an incumbent but only barely: He first won his seat in a special election earlier this year. Mr. Green currently represents the Ninth District, which was gerrymandered to elect a Republican, and is seeking renomination in the 18th, which includes portions of his current district.

A wave of crypto spending on behalf of Mr. Menefee and against Mr. Green has influenced the race. Mr. Green has been a critic of the industry and sits on the powerful House Financial Services Committee.

Can national Democrats stop one of their own they say is antisemitic?

In yet another Democratic face-off, Johnny Garcia, a Bexar County sheriff’s deputy, has the look, on paper at least, of a candidate who should be coasting to victory in his runoff in the 35th Congressional District on Tuesday.

The Democratic candidate has been endorsed by the national party’s House campaign arm, by Mr. Talarico and by the Blue Dog Coalition, a group of moderate Democrats in the House.

His rival, Maureen Galindo, is a sex therapist and left-wing activist who has suggested an immigration detention center be turned into “a prison for American Zionists,” which Democrats have denounced as “straight out of the Nazi playbook.”

Yet Ms. Galindo has been lifted by nearly $900,000 in spending from a secretive super PAC that has reported no donors but has loose ties to Republicans and has been meddling in Democratic races.

Ms. Galindo finished first in the initial election in March. Democrats believe Mr. Garcia could compete for the seat in November, even though Republicans drew it to elect a Republican in their redistricting gambit last year.

A Democratic showdown in Dallas

When Colin Allred vacated his congressional seat in 2024 to run for Senate — he lost to incumbent Ted Cruz — his career in the House of Representatives seemed over. But after he initially tried running for Senate again this cycle, he decided his chances of serving again would be stronger if he ran for the House.

That decision has put him on a collision course with his successor, Representative Julie Johnson.

The race has been marked by some of the same racial dynamics of the Senate primary that Mr. Allred exited. Mr. Allred is Black and Ms. Johnson is white. Mr. Allred supported Representative Jasmine Crockett, who is Black, in the Senate race; Ms. Johnson endorsed Mr. Talarico, who is white, before Ms. Crockett entered the race. Mr. Talarico defeated Ms. Crockett by a six-point margin.

Adding to the tension was recent audio of Ms. Johnson dismissing another Black member of the delegation, Representative Marc Veasey, as a lawmaker holding a safe Democratic seat and “not doing a damn thing.”

Two conservatives vie to be Texas’s top cop

One of the other key races on Tuesday is a runoff for the Republican nomination to replace Mr. Paxton as the state attorney general, a powerful post that he used to raise his national profile.

The contest pits Mayes Middleton, a conservative state senator, against Representative Chip Roy, who has carved a reputation as a hard-liner on Capitol Hill but who at times has split with Mr. Trump, including in the aftermath of the Jan. 6, 2021, riot.

Mr. Roy is a former top aide for Senator Ted Cruz, who has backed his candidacy.

Mr. Middleton contributed $3 million to his own campaign; Mr. Roy was supported by $2.75 million from Alex Fairly, an Amarillo businessman.

The Democrats will also hold a runoff Tuesday between Nathan Johnson, a state senator, and Joe Jaworski, a former mayor of Galveston. Republicans are heavily favored in November.