Texas Senate Republican Primary RunoffJohn Cornyn, the incumbent senator, is facing a competitive challenge from Texas’s attorney general, Ken Paxton. Neither candidate received a majority of votes in the March primary election, forcing the runoff. President Donald Trump has endorsed Paxton, a major blow for Cornyn, who has represented the state since 2002. Still, Cornyn has received much support from prominent members of the G.O.P., including Senate Majority Leader John Thune and Rick Perry, the former Texas governor. Before serving in the Senate, Cornyn was the state’s attorney general and served as a justice on the Texas Supreme Court.Paxton first gained national attention when he sued four key battleground states in an attempt to overturn Joe Biden’s 2020 election victory. He has also been the subject of several scandals during his tenure. In 2015, he was indicted on two counts of securities fraud and one count of failing to register as an investment adviser with state regulators. In 2024, after more than eight years of delays, Paxton agreed to pay nearly three hundred thousand dollars in restitution and to perform a hundred hours of community service, without admitting wrongdoing. In 2023, Paxton was also accused of abusing his office to assist in the case of Nate Paul, a real-estate developer and a donor to Paxton’s campaign who was separately charged with wire fraud and making false statements on loan applications. Paul had allegedly helped fund a renovation of Paxton’s Austin home and had hired a woman with whom Paxton was reportedly having an extramarital affair. Paxton was impeached by the Texas House before being acquitted by the state Senate. In addition to Trump’s endorsement, he has received support from other major MAGA figures, including Steve Bannon, Laura Loomer, and Ted Nugent. Ted Cruz, the other Texas senator, and Greg Abbott, the state’s governor, have declined to endorse either candidate.The runoff’s winner will face the Democrat James Talarico, a state representative and former public-school teacher, whose long-shot bid for the Senate has generated national attention.Texas Congressional Primary RunoffsThe primary for Texas’s Thirty-fifth Congressional District, in which Maureen Galindo, a housing advocate and a sex therapist, is facing Johnny Garcia, a local sheriff’s deputy, has recently gained national attention. Galindo, in criticizing ICE detention centers, said in a post on Instagram that a local immigration facility should be turned into “a prison for American Zionists and former ICE officers for human trafficking.” Galindo added that the facility should be “a castration-processing center for pedophiles, which will probably be most of the Zionists.” Galindo has insisted that she is not antisemitic, and told a radio show she was opposed only to “Zionist Jews”; she later said in a video that “putting billionaire zionists in prison DOES NOT MEAN putting all Jews in internment camps.” She has also said that Garcia should be tried for treason over his support for Israel. Democrats have distanced themselves from Galindo, with the Democratic Senate candidate, James Talarico, endorsing Garcia and calling Galindo’s remarks “antisemitic.” The House Minority Leader, Hakeem Jeffries, has accused the G.O.P. of supporting Galindo through a political-action committee, in an attempt to make the general-election matchup more favorable for Republicans.