Walsh, a Republican who represented Illinois in the House and has been a Trump critic, added he isn't accusing Trump of treason. But he said Trump "betrayed our country again this week" by calling on China and Ukraine to investigate one of his chief political rivals in the 2020 presidential race, former Vice President Joe Biden.

"This president deserves to be impeached," Walsh said.

House Democrats have launched an impeachment inquiry into Trump's efforts to push Ukraine's government to investigate Biden and his son Hunter. But the House has not held a formal vote on an impeachment inquiry, and several Democrats on Sunday brushed off calls for a vote.

Though both Walsh and Sanford are running long-shot bids to replace Trump as the GOP standard-bearer in the 2020 presidential election, the pair differed on whether Trump should be impeached.

"I respectfully disagree. In other words, the nature of the process is not to come to the conclusion at the beginning of it," Sanford said. "And for people to just step out and say he needs to be impeached is to actually diminish and discard with the very process that is laid out by our Founding Fathers."

"And so I do think we ought to be incremental," Sanford said. "But to jump to conclusions and say, he needs to be impeached, what he's done is treasonous, is to say, we're not going through the very process that the Founding Fathers laid out."

Asked whether he'd vote to open an impeachment inquiry against Trump, Sanford responded, "I suspect so." But he added that he doubts impeaching Trump would be the right move.

"I would ultimately, as I have said previously, I don't know that, ultimately, impeachment is the best way to go," Sanford said. "I think probably censure is, given the fact that we're this close to an election. But that's a larger conversation."

Pressed on whether he would vote for Trump in the 2020 election, Sanford said he didn't know and would make his decision based on the issues "with particular regard to debt and deficit and government spending."

Walsh, meanwhile, said, "There is no way in hell" he'd vote for Trump in a general election.

"The election is about Trump, period," he said.