Paula Barche Rupnik, a Republican from Scottsdale, Ariz., was planning to vote for Senator John McCain in his re-election campaign this year. But she changed her mind this weekend, after he rescinded his support for Donald J. Trump.

Instead, she plans to split her ticket, voting for Mr. Trump, the Republican presidential nominee, but for Mr. McCain’s Democratic challenger, Representative Ann Kirkpatrick.

She has never voted for a Democrat before.

“I want to send a message to John McCain,” said Ms. Rupnik, 58, a consultant for an essential oils company. “If he doesn’t get elected, the American people that support Trump are going to blame it on those Republicans who didn’t support him.”

Ms. Rupnik’s punitive impulse captures the dilemma confronting Republican leaders as they head into the final four weeks of the campaign.