Rep. Trey Gowdy, chairman of the House Oversight and Government Committee, believes President Trump's lawyers are not doing him any favors by "allowing" the investigation into Russian influence on the 2016 U.S. presidential election "to be framed as an investigation into collusion, and collusion only."

"I think his lawyers have done a disservice to him, frankly," the South Carolina Republican told CBS News chief White House correspondent Major Garrett on the latest episode of "The Takeout" podcast.

President Trump and his lawyers have consistently maintained his campaign did not collude with Russians to win the election. Gowdy thinks the focus should be directed elsewhere.

Over breakfast at District Taco in the Capitol Hill neighborhood of Washington, Gowdy pointed to Deputy Attorney General Rod Rosenstein's original statement on the appointment of Robert Mueller to be special counsel last May. The statement said Mueller would "serve as Special Counsel to oversee the previously-confirmed FBI investigation of Russian government efforts to influence the 2016 presidential election and related matters."

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"So from my standpoint, the foundational inquiry is, what did Russia do with respect to the 2016 election process? And if there's criminality, of course we expect him to find it. But the notion that he was hired to only go look for criminality I think does a disservice to him," Gowdy explained.

Gowdy said he stands by his public advice to President Trump Sunday: If he is innocent, he should act like it.

"There's a certain level of frustration that comes from anyone who is, quote, under investigation," he explained. "If you believe you've done nothing wrong, you want the investigation concluded as quickly as possible. It is beyond argument that this has cast a pall over the first part of his presidency."

"If you're the investigator, you're saying, you know what? I have an obligation to run out all the witnesses and access all the documents and give you the definitive word and we're not on a time schedule, so there's tension."

Gowdy, who served for six years as a federal prosecutor, said President Trump has a unique attitude for someone in his position.

"The president talks more than any target of any investigation that I've ever participated in," he observed, noting that he's never met President Trump or had a conversation with him. "I mean, for the most part you have a hard time getting the target to talk at all."

But Gowdy doesn't believe Mr. Trump will end up firing special counsel Robert Mueller, despite his heated Twitter rhetoric on the matter last weekend.

"I don't think he can," Gowdy said.

For more of Major's conversation with Rep. Trey Gowdy, including why he doesn't think President Trump can fire Mueller, download "The Takeout" podcast on Apple Podcasts, Google Play, Stitcher, or Spotify. New episodes are available every Friday morning.

Also, you can watch "The Takeout" on CBSN Friday and Saturday nights at 9pm ET/PT. For a full archive of "The Takeout" episodes, visit www.takeoutpodcast.com. And you can listen to "The Takeout" on select CBS News Radio affiliates (check your local listings).

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Producers: Arden Farhi, Katiana Krawchenko