The Republican embrace of President Donald Trump is beginning to show cracks as some rank-and-file GOP lawmakers stepped up their criticism of the president back home in their districts in a week where his former personal lawyer and onetime campaign chairman pleaded to and were found guilty of eight federal crimes apiece.

No one is jumping to conclusions yet about whether Trump should face impeachment. But some Republican lawmakers have been candid in recent days about the prospect of impeaching the president, and what would need to happen for them to consider such a step.

“We’ve got to wait for the investigations to finish, House, Senate, and more,” North Carolina Rep. Walter Jones, who hasn’t shied away from responding sharply to Trump’s controversial remarks in the past, told WITN. “At whatever point, if it’s justified, that they recommend impeachment, then that would be on the table.”

In a series of tweets Thursday, Michigan Rep. Justin Amash said the criminal allegations against Trump are “serious and should be taken seriously, especially by members of Congress.”

Many of the allegations against @POTUS are serious and should be taken seriously, especially by members of Congress.

— Justin Amash (@justinamash) August 23, 2018

He echoed Jones’ notion that lawmakers should wait until special counsel Robert S. Mueller III concludes his investigation into the 2016 Trump campaign’s possible ties to Russia and the other crimes it has uncovered through the course of that investigation before the House considers impeachment in earnest.

“We don’t impeach simply because we dislike a person or disagree with his policies. If you’re unhappy about [the president], then don’t vote for him in 2020,” Amash wrote. “The electoral process should determine who holds the executive power.”

Amash said he felt it was important for lawmakers to “share their thoughts” on how they perceive the impeachment process as both a “quasi-legal” and “quasi-political” tool.

At a town hall event in his upstate New York congressional district this week, Rep. John Katko fielded multiple questions about Trump and impeachment.

Katko said it’s “dangerous” to speculate before the investigation has wrapped up but that he will “abide by the facts wherever they lead us,” the Auburn Citizen reported.

“I’m not saying he’s innocent. … I’m not saying he’s guilty,” Katko said.

Later in that town hall, Katko read off a list of times he has disagreed with the president to prove his independence from the White House line.

Katko has previously disputed the president’s claim that the special counsel’s probe was a “rigged witch hunt.”

The prospect of impeachment looms large over many House members this November, when voters head to the polls for the midterm elections that will decide whether the GOP keeps its majority in the chamber or if Democrats wrestle away control.

Jones believes Republicans, as it stands, are in “deep political trouble.” But if Republicans are swamped by a so-called blue wave, it won’t be the fault of the candidates the party has put forth.

“The sad thing is, it’s not so much what we have done as a party, but what the head of the party in the White House has done,” Jones said.

Even some Republican leaders are urging members to be cautious in their support of Trump.

Former National Republican Congressional Committee Chairman Tom Cole warned candidates not to rush to the president’s defense in case more incriminating information comes out about the president and they have to eat their words.

“Where there’s smoke, and there’s a lot of smoke, there may well be fire,” Cole reportedly told Republicans, according to The New York Times.

“Anybody who says this is not disturbing is not being honest,” the former House Republican campaign chairman said. “My advice to any candidate would be: Keep your powder dry and don’t rush to attack or defend anybody because you just don’t know enough to have a reaction that you can still defend three months from now.”

Jones is one of seven Republicans to back an iteration of a measure introduced in the House to prevent Trump from arbitrarily ending the Mueller investigation.

He is joined by GOP Reps. Charlie Dent, Brian Fitzpatrick, Ryan A. Costello, Ileana Ros-Lehtinen, Leonard Lance and Mike Coffman.

Watch: ‘President Did Nothing Wrong,’ Sanders Says