On Saturday, Ms. Cheney said that she asked Mr. McMurtry’s campaign to return her contribution.

“We as Republicans must not condone racism in any form,” Ms. Cheney wrote on Twitter. “Last night I was alerted to tweets by a candidate to whom my political action committee made a contribution. After reviewing the tweets, I asked that the contribution be returned.”

Mr. Turner and the Republican Jewish Coalition also said in statements on Saturday that they had requested for the campaign to return their donations. The Republican Jewish Coalition also rescinded the endorsement of Mr. McMurtry it made hours after Mr. Massie tried to force a vote on the coronavirus relief package.

Mr. Massie has long clashed with hawkish Republicans like Ms. Cheney, and he alluded to his disdain for their worldview on Twitter after her donation to Mr. McMurtry and that of Mr. Turner’s became public, writing: “I guess #neocons really do hate coming to work, while expecting nurses and truckers and soldiers to keep doing their jobs. Who knew?”

Mr. Massie’s race is less than two months away. After his move to force a vote on the stimulus bill, what was considered a sleepy race has been injected with a shot of intrigue. Mr. Trump sent out two hostile tweets targeting the Kentucky Republican, branding him “a third rate Grandstander” and calling for him to be thrown out of the party.

Mr. Massie, who was at home in Garrison, Ky., on Friday, said that he had spoken by phone with the president hours beforehand and that Mr. Trump had “articulated that it wasn’t a good political move.” He knew by proceeding that he was in danger of subverting one of his campaign strategies — to keep Mr. Trump out of the race.

“The only way that my opponent could get any traction was to get support from President Trump,” he said, noting Mr. Trump has a 96 percent approval rating among likely Republican primary voters in his district.

Mr. Massie has made no apologies for insisting that lawmakers should show up in person to record their votes on the behemoth spending package. But in the interview on Friday, he said he would not object to forgoing a floor vote on a change to House rules that Democratic leaders have embraced to allow for voting by proxy during the pandemic — so long as the process was sufficiently “transparent.” Mr. Massie said the rule should require that the names of those who voted in person and who voted by proxy be made public, along with the names of those whom absent lawmakers had authorized to vote on their behalf.