Republican senators reacted angrily on Tuesday to President Trump’s decision to endorse Ken Paxton, the Texas attorney general, in the state’s Senate primary runoff, warning that his snub of the incumbent Senator John Cornyn could risk the seat and the party’s fight to keep its majority.

Heading into their weekly G.O.P. luncheon not long after Mr. Trump posted his choice on social media, many Senate Republicans appeared stunned and livid as they learned the news, which dealt a serious blow to Mr. Cornyn, who has served for more than two decades.

“Oh boy,” said a visibly dismayed Senator John Hoeven of North Dakota, as he left the Senate chamber after hearing of Mr. Trump’s announcement.

“Well, obviously,” he added, “I support Senator Cornyn.”

A stone-faced Senator Roger Wicker of Mississippi refused to answer questions about the endorsement as he exited the chamber following a vote.

Senator Lisa Murkowski, the Alaska Republican whose independent streak has often angered the president, said that she was “supremely disappointed” by Mr. Trump’s decision.

Then she went a step further, saying that the president’s endorsement of Mr. Paxton, a scandal-plagued conservative firebrand, could cost Republicans what had been considered a safe Senate seat.