Democrats have launched a formal impeachment inquiry, over concerns the president pressured Ukraine to investigate Joe Biden and his son.
The ensuing scandal has placed Republicans in a politically precarious situation.
“Everyone is getting a little shaky at this point,” said Brendan Buck, who was previously an aide to Paul Ryan, the former House Speaker.
“Members have gotten out on a limb with this president many times only to have it be cut off by the president.
“They know he’s erratic, and this is a completely unsteady and developing situation,” he added, according to The Washington Post.
According to the newspaper, few Republicans want to strongly defend the White House publicly, because they doubt the credibility of the president’s claims.
Mr Trump has called on China and Ukraine to investigate Joe Biden, the Democratic 2020 frontrunner, despite the fact that it is illegal in the US to ask for a foreign country to interfere in an election.
A whistleblower complaint about the president’s conduct was met with outrage by Democrats and lies at the heart of the impeachment inquiry.
A second complaint has reportedly been made, intensifying the inquiry.
Recent polls show an increase in Americans supporting impeachment, with 48 per cent of those polled backing the measure, and 46 per cent opposing it.
Despite this, just three Republicans from the senate have publicly criticised the president over his behaviour.
“I thought the president made a big mistake by asking China to get involved in investigating a political opponent,” she said.
Ms Collins did not declare support for the president’s impeachment but said she hoped the process “will be done with the seriousness that any impeachment proceeding deserves.”
Mitt Romney and Ben Sasse have also spoken out against Donald Trump.
Mr Romney, the senator for Utah, said the president’s appeal to China and Ukraine was “wrong and appalling” in comments made last week.
In a statement to the Omaha World-Herald newspaper, Ben Sasse, senator for Nebraska, echoed Mr Romney’s condemnation.
“Hold up: Americans don’t look to Chinese commies for the truth,” he wrote.
“If the Biden kid broke laws by selling his name to Beijing, that’s a matter for American courts, not communist tyrants running torture camps.”
On Thursday a voter confronted Joni Enrst, senator for Iowa, for “not standing up” to the president.
“You still stand there silent. And your silence is supporting him in not standing up,” Amy Haskins, an Iowa resident, said.
“Where is the line? When are you guys going to say ‘Enough,’ and stand up and say, ‘You know what? I’m not backing any of this.”
Ms Ernst replied: “The president is going to say what the president is going to do.”
Some senators, conscious of widespread support for Mr Trump among Republicans, have struck a more cautious note.
Marco Rubio, the senator for Florida, dismissed the president’s China comments as a joke.
“I don’t know if that’s a real request or him just needling the press, knowing that you guys were going to get outraged by it,” he told a group of journalists.
The silence from most Republicans have angered Democrats, who believe the president’s behaviour constitutes a brazen abuse of power.
“My Republican colleagues’ silence seems unsustainable and inexcusable, given the threat to our national security as well as the integrity of our democratic institutions,” said Richard Blumenthal, the senator for Connecticut.
During the Senate stage of an impeachment process, senators conduct a trial presided over by the Supreme Court’s chief justice.
If two-thirds of senators find the president guilty of impeachable offences, he is removed and the vice president replaces him.
No US president has ever been removed from office through the impeachment and conviction process.