A video mocking what the campaign views as Democrats’ obsession with impeachment was released within 30 minutes. “We’ve had that ready for weeks in case the Democrats were that dumb,” one campaign aide said.

On Wednesday, most Republicans publicly projected similar confidence. But the private reactions were more reserved as the White House released the rough transcription of a July phone call between Mr. Trump and President Volodymyr Zelensky of Ukraine that discussed Democratic presidential candidate Joe Biden and is central to the impeachment inquiry.

“Pretty damning,” said one Republican close to the White House. “Not great,” another Trump political adviser said…

“This will have no impact on the president’s supporters, and it will keep Democrats trapped in a cul-de-sac where they’re walking around chanting impeach-impeach-impeach,” said Newt Gingrich, a Trump ally and former House speaker who lost his job after leading the impeachment of then-President Clinton. “And in my experience with that, it doesn’t quite work.”