Mr. Flake is not the Senate’s only vulnerable Republican; Senator Dean Heller of Nevada is also facing a tough re-election race. And Republicans will now have to field a candidate to succeed Mr. Corker, who announced late last month that he was not running next year.

Last weekend, Mr. Corker said his concerns about Mr. Trump were shared by nearly every Senate Republican, even if few have spoken out. Mr. Flake, by contrast, has put pen to paper with his criticism; his new book, “Conscience of a Conservative,” published in August, is a blistering indictment of the Republican Party and of a president who, despite record-low overall approval ratings, has retained the support of about 80 percent of his party.

Mr. Flake’s main primary challenger at the moment, Kelli Ward, made clear in an interview that she intended to paint Mr. Flake as “an obstructionist to the America First agenda that Donald Trump touted on the campaign trail, and that the American people want to see enacted.”

Ms. Ward, an osteopathic physician and a former state senator who ran unsuccessfully against Arizona’s other senator, John McCain, in 2016, was busy preparing last week for her campaign kickoff. It is scheduled for Tuesday night with the conservative radio host Laura Ingraham as the featured guest.

Andy Surabian, senior adviser to the Great America Alliance, a Trump-aligned group whose political action committee has been supportive of Ms. Ward, said Mr. Flake’s troubles were “entirely self-inflicted.”

“If Flake wants to know why he’s vulnerable, all he needs to do is look in the mirror,” said Mr. Surabian, who had a stint in the White House as deputy to Stephen K. Bannon, Mr. Trump’s former chief strategist. He added: “No one told him to go out and be the face of the anti-Trump resistance in the Republican Party. No one told him to go out and write a book that was basically an anti-Trump screed. The reason the race is in play is because of Jeff Flake’s actions.”