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While at a groundbreaking event in Lubbock, Texas, Sen. John Cornyn issued a warning to Texas voters about state Attorney General Ken Paxton — hours after President Donald Trump endorsed Paxton."I believe that in terms of our success in November, that Ken Paxton would be an albatross around the neck of our candidates and would likely lose to James Talarico," Cornyn said Tuesday, May 20. "I think we've come too far and worked too hard to risk that."The runoff has grown increasingly bitter with both Cornyn and Paxton publishing personal and political attack ads against one another, as a May poll shows Paxton leading Cornyn — but only narrowly.Cornyn also noted that Republicans have "family fights" within the party but ultimately unify to win the November General Election.At an event in Lubbock later that day, Cornyn was asked whether he had spoken with Trump following the endorsement. He replied no and said that, even though he didn't receive the highly sought-after endorsement, he's not giving up the fight."I know who gets to choose our senators, and it's the people of Texas and there's no substitute for that," Cornyn said.Why did Trump not endorse Cornyn?Trump said in his endorsement post that Cornyn is a "good man," but cited the senator's lack of support for him when "times were tough" and his late backing during Trump's 2024 presidential run as why he chose not to.Cornyn responded to the president's statement, saying he has worked closely with Trump during both presidential terms and voted with him more than 99% of the time."He has consistently called me a friend in this race," the statement read. "It is now time for Texas Republican voters to decide if they want a strong nominee to help our GOP candidates down ballot and defeat Talarico in November, or a weak nominee who jeopardizes everything we care about. I trust the Republican voters of Texas."Mateo Rosiles is the Texas Connect reporter for USA TODAY and its regional papers in Texas. Got a news tip for him? Email him at mrosiles@usatodayco.com.