Republican Senator Jeff Flake has compared Donald Trump's behaviour to that of 1950s demagogue Joseph McCarthy, saying "you can't continue to just remain silent" about the US leader's politics.

Key points: Senator Flake said he hopes the "tipping point" on Mr Trump's behaviour is coming

Senator Flake said he hopes the "tipping point" on Mr Trump's behaviour is coming Mr Trump has been exchanging insults with Senator Flake and Senator Bob Corker

Mr Trump has been exchanging insults with Senator Flake and Senator Bob Corker Mr Trump said yesterday's meeting with other Republican senators was a "love fest"

The Arizona senator made the rounds of morning television news shows to talk about his decision not to run for re-election in 2018 and his impassioned speech on the Senate floor yesterday, in which he said he could no longer be "complicit" with the Republican President.

"There is a tipping point ... I hope we're reaching that tipping point," Senator Flake told NBC's Today program.

Senator Flake cited the era of McCarthy, the Republican Wisconsin senator whose smear tactics alleging Communist infiltration ultimately led to his censure.

In an opinion column in The Washington Post, Senator Flake quoted Joseph Welch, an Army lawyer, who stood up to McCarthy in a June 1954 hearing and demanded: "Have you no sense of decency, Sir?".

"The moral power of Welch's words ended McCarthy's rampage on American values, and effectively his career as well," he wrote.

"We face just such a time now. We have again forgotten who we are supposed to be."

Senator Flake also said he thinks more of his Republican colleagues will speak out, he told the American ABC's Good Morning America program.

"It's up to us to stand up and say, 'this is not acceptable'," he said.

In an interview with MSNBC, Senator Flake said: "We are excusing undignified and outrageous and reckless speech and behaviour as 'telling it like it is' ... That's not right."

Mr Trump immediately fired back at Senator Flake and fellow retiring Senate Republican Bob Corker on Twitter, saying the two weren't running for re-election because "they had zero chance of being elected".

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Mr Corker had previously labelled Mr Trump "untruthful" and accused him of debasing the nation.

Mr Trump also contended that Senators Flake and Corker stand alone, boasting in several tweets that he had gotten standing ovations at a Senate Republicans' luncheon on Tuesday at the Capitol.

Asked why others in his party haven't yet done so, Senator Flake said "fatigue" was to blame.

He stopped short of saying Mr Trump should be declared unfit for office or impeached.

"The voters made their choice," Senator Flake said. "He was elected fair and square."

Party rallies behind tax cuts despite criticism

Sorry, this video has expired Republican politicians take aim at Donald Trump

Congressional Republicans showed scant signs of turning on Mr Trump, rallying instead behind their party's tax-cutting plans.

"I just think that right now our members are pretty well convinced that we need to put some points on the board, get some wins," said Senator John Thune of South Dakota, a senior Republican leader.

"So I think the cohesion in the conference right now is pretty strong, particularly on the issue of tax reform."

While Senators Flake and Corker's comments produced a day of high drama and underscored Republican Party divisions, there was no evidence that they had caused a broad shift that could derail the party's legislative agenda.

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"We're all professionals here," said Senator David Perdue.

"These two guys can say and do what they want to do. But right now, we've got a bigger issue, and the bigger issue is to get this tax bill done."

Asked whether the senators' discontent could make it harder for Republicans to push their tax cuts through Congress, Senator Thune said: "Everybody gets to vote the way they want to vote, but both of them are very conscientious and principled and want to do the right thing."

Even so, Senator Flake was making no promises about backing the still evolving tax package, which could make federal deficits far worse.

"I don't expect to be voting differently than I would before," he said.

"Certainly on this tax bill, for example, I know that a lot of us are very concerned about the debt and deficit and want to make sure this is actually tax reform and not just a tax cut."

Sorry, this video has expired Bob Corker takes aim at 'untruthful' Donald Trump

Senator Lindsey Graham, a critic of Mr Trump during the 2016 presidential campaign who's been working with him on health care and other issues, said his focus was on legislative accomplishments.

"I'll stand up when I need to, but I'm trying to get taxes cut, Obamacare repealed and win a war we can't afford to lose," he said.

Senator Susan Collins said politicians must "distinguish between the President's policy agenda and his approach to governing."

She is a moderate who helped block the party's drive to annul the Obama-era health care law.

"There have been many of us for a long time who have had concerns about his approach to governing," Senator Collins said.

"But I accept the fact that he is President now. We need to learn to work better together and respect the roles that each of us have to play."

Bob Corker campaigned with Donald Trump during last year's election. ( Reuters: Joshua Roberts )

AP