“As I watched him on ‘Face The Nation,’ what he said was pretty clear from my perspective,” said Senator Tim Scott, Republican of South Carolina and a close friend of Mr. Gowdy’s. “He put the memo in one tranche and put the Russia investigation in another tranche, and I think one doesn’t cancel out the other.”

To be sure, the tumult around the memo has had an impact. It has helped bolster the views of Mr. Trump’s most vociferous partisans who insist that the Russia investigation was started under false pretenses by an F.B.I. leadership that favored Hillary Clinton and is hopelessly biased against Mr. Trump. The president has fed that notion with a steady stream of tweets, such as, “Their was no Collusion and there was no Obstruction (the word now used because, after one year of looking endlessly and finding NOTHING, collusion is dead). This is an American disgrace!”

And the attention on the spectacle surrounding the memo has taken the public’s eye off the Russia investigation itself.

In that sense, Mr. Gowdy’s public protestations against the president’s conclusions are contradicted by his private involvement in the drafting of the memo.

But in Republican circles, Mr. Gowdy’s words matter.

“I don’t think that Trey was looking to contradict anybody,” said Representative Thomas J. Rooney, Republican of Florida. “I think that Trey speaks from a place of judicial and lawyerly knowledge that a lot of people don’t have or comprehend.”

Mr. Gowdy, 53, is best known on Capitol Hill for two things: his ever-shifting hairstyles and for the way he grilled Mrs. Clinton while leading the House inquiry into the 2012 attacks on Benghazi, Libya. He has a tendency to proclaim bipartisan intentions to reporters before carving up his political opponents.

Close observers of Mr. Gowdy see him as a man in tension with himself. He is smart about politics and almost certainly knew that the release of the memo — known as the “Nunes memo” after Representative Devin Nunes, Republican of California and chairman of the House Intelligence Committee — would become fodder for Republicans, including Mr. Trump, to undercut the Mueller investigation.