Donald J. Trump’s supporters in Congress have struggled for weeks with a daily deluge of questions from reporters about the latest comments by the Republican Party’s standard-bearer.

But this week seemed to be a turning point.

Instead of defending Mr. Trump, people like Senator Bob Corker, Republican of Tennessee and a rumored vice-presidential contender, told reporters that he was disappointed with Mr. Trump’s call for a sweeping ban on Muslim immigrants and for intensive profiling of Muslim citizens in the United States.

Senator John Cornyn, Republican of Texas and the No. 2 in Senate leadership, said, “I just don’t have enough time to provide running commentary for everything a candidate running for president says.” Mr. Cornyn, citing scheduling, said he would not attend Mr. Trump’s events in Texas on Thursday.

Even Representative Duncan Hunter, Republican of California and the co-chairman of Mr. Trump’s House Leadership Committee, sought some distance from him. “I am not a surrogate,” he told The Hill.