Jack Langer, a spokesman for Nunes, downplayed the comments in a statement to CNN, saying "it's unsurprising to see the left-wing media spin Chairman Nunes' routine observations as some nefarious plot, since these same media outlets spent the last year and a half touting non-existent Russia collusion conspiracy."
Maddow said on Wednesday that the audio, which MSNBC described as a "secret audio recording," was obtained by a progressive group called Fuse Washington after one of its members paid to attend a private fundraiser held last week for Rep. Cathy McMorris Rodgers, a member of House GOP leadership.
The Nunes-led House Intelligence Committee conducted a yearlong investigation of Russia's election interference. The committee's Republicans issued a report that stated they found no evidence of collusion between Trump's team and Russia, but Democrats accused Republicans of failing to interview witnesses and subpoena key documents in the probe in an effort to protect Trump.
Democrats on the committee have continued their own investigation and have made clear they will ramp up the probe again should they retake the House in November.
"If we actually vote to impeach, what that does is that triggers the Senate then has to take it up," Nunes said on the audio, adding, that the "Senate only has so much time."
Nunes said he thinks Rosenstein "deserves to be impeached," but noted that "the Senate would have to drop everything they're doing and start to, and start with impeachment on Rosenstein. And then take the risk of not getting Kavanaugh confirmed." He added, "so it's not a matter that any of us like Rosenstein. It's a matter of, it's a matter of timing."
Nunes' comments on the timing of an impeachment fight echo what House Speaker Paul Ryan, who does not support the impeachment push, has publicly said.
Ryan said in July, "if this were to pass through the House, then what it would do is tie the Senate into knots ... That means it would derail or largely delay a big part of our agenda ... and it would clearly dramatically delay the confirmation of Brett Kavanaugh to go to the Supreme Court," he said.
CNN's Sarah Westwood, Jeremy Herb and Manu Raju contributed to this report.