WASHINGTON — It was a straightforward question being put to nearly every Republican senator in the Capitol on Thursday: Should the Senate consider new evidence as part of the impeachment trial?

But when Manu Raju of CNN, a longtime congressional reporter, put it to Senator Martha McSally of Arizona, a first-term Republican who is up for election this fall, she went on the attack.

“You’re a liberal hack,” she said. “I’m not talking to you. You’re a liberal hack.”

She posted a video of the exchange on Twitter, earning plaudits from President Trump’s allies, including the Fox News host Sean Hannity.

And @TrumpWarRoom, a Trump 2020 account, congratulated Ms. McSally — “THIS is how you handle FAKE NEWS,” the account wrote — and urged followers to donate to her re-election campaign.