a rising star in her fourth term who has long toiled to increase the number of women in the Republican ranks and has more recently become a fierce defender of Mr. Trump.

Ms. Stefanik, 36, has begun reaching out to Republican lawmakers to gauge their support, according to two people familiar with the private conversations, and by Tuesday evening, one of her political aides was retweeting speculation that she would “make an outstanding conference chair.”

Representative Guy Reschenthaler of Pennsylvania, a member of the Republican leadership who initially whipped votes for Ms. Cheney, said that he was counting potential votes for Ms. Stefanik and believed the job would be hers if she ran.

Republicans have also floated Representative Jackie Walorski of Indiana as a possible alternative. As the top Republican on the Ethics Committee, Ms. Walorski this year successfully balanced the job of condemning Representative Marjorie Taylor Greene’s past conspiratorial statements while arguing she should not be kicked off her committees.

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