Washington (CNN) President Donald Trump's feud with GOP Sen. Bob Corker re-erupted Tuesday, threatening to sour an effort to pull the President and Capitol Hill Republicans together to spark momentum behind a crucial push for tax reform.

The President accused the Tennessee senator of enabling President Barack Obama's Iran deal -- shading the facts on that issue -- and of now fighting tax cuts.

Bob Corker, who helped President O give us the bad Iran Deal & couldn't get elected dog catcher in Tennessee, is now fighting Tax Cuts....

...Corker dropped out of the race in Tennesse when I refused to endorse him, and now is only negative on anything Trump. Look at his record!

"Bob Corker, who helped President O give us the bad Iran Deal & couldn't get elected dog catcher in Tennessee, is now fighting Tax Cuts," Trump said, adding "Corker dropped out of the race in Tennesse when I refused to endorse him, and now is only negative on anything Trump. Look at his record!"

Corker tweeted right back at Trump.

"Same untruths from an utterly untruthful president. #AlertTheDaycareStaff," he wrote in a biting tweet.

This latest dust-up comes as Trump is set to attend lunch Tuesday with lawmakers he spent much of the summer blasting for failing to enshrine his political agenda. Some have been critical over his chaotic, unpredictable method of governing, but Trump hopes to woo them to finally rack up a genuine legislative win on tax reform.

The atmosphere will be especially charged because a number of Trump's hosts fear a 2018 primary challenge from populist, nationalist candidates in his own image, being recruited by his erstwhile political guru Stephen Bannon . Others, like Corker, have questioned Trump's fitness to serve as commander in chief.

While the meeting will highlight political and temperamental divides between Trump and Majority Leader Mitch McConnell and his troops, both sides have enough at stake to bury their mutual resentment and work together.

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The President needs a win to avoid the embarrassment of a barren first year of his term that has undercut his claims to be the ultimate deal-maker and raised doubts about his capacity to deliver on big campaign promises. Establishment Senate Republicans are even more desperate, striving for an achievement to appease GOP primary voters that could blunt the attacks of Bannon's shock troops in his "season of war" against his own party.

Sen. John Thune, a member of the Senate Republican leadership, told CNN's Ted Barrett that Trump would do well to show the senators he wants to be a "constructive partner" in the wake of a truce that emerged after a joint news conference between the President and McConnell in the White House Rose Garden last week.

"If you have people running for re-election next year ... the best thing you can go back and talk about is that you'd gotten results. I think to the degree that President delivers that message, it will be very well received by Republican senators," Thune, of South Dakota, said.

Sen. David Perdue, a Georgia Republican, told CNN the President did not need to make a "rah-rah" speech but should make the point that the challenge before Republicans was bigger than tax reform -- it was about their capacity to improve their lackluster performance to show they could govern.

"People back home are apoplectic that the Republican Senate is not backing this President's agenda ... People didn't elect Donald Trump because they are enamored with Congress. Just the opposite, I believe. That's how I was elected," Perdue said.

And Louisiana Republican Sen. John Kennedy told CNN's Lauren Fox he would like to hear a commitment from Trump that he will go to the mat selling whatever the tax plan is to the American public.

"What I'd like to hear from the President is first of all what his priorities are. I mean everyone knows what the buffet looks like, but we can't all have a dish of everything," he said. "I'd like to see him make as many visits to as many states as he possibly can and for the next three months I'd like to hear him talk about three things: tax reform, tax reform and tax reform."

Health Care 2.0?

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But the magnitude of the tax reform push is already raising questions about whether the White House and Hill Republicans can avoid the discord that turned the party's health care push earlier this year into a disaster.

Trump so far has adopted a similar approach to the failed Obamacare effort, talking up the historic nature of the tax legislation and lacing it with superlatives but also again giving the impression he is not up to speed with the policy details.

For instance, he President told GOP House members on a conference call on Sunday that they were "on the verge of doing something very, very historic" after promising Fox Business News in an interview "the biggest tax cuts ever, in the history of this country."

But he also warned in the call that if Capitol Hill Republicans did not pass a tax bill, they will face defeat in the midterm elections in November 2018, a congressional source told CNN's Jamie Gangel.

But aside from a pledge to cut corporate taxes to 20%, calls to abolish the estate tax and a simplification of tax brackets, much remains unknown about the nuts and bolts of the tax plan.

It's reminiscent of the Obamacare repeal debacle.

Just a few months ago, Trump was promising "wonderful" health care, with lower deductibles, lower premiums, better care and coverage for all, promises that he found impossible to reconcile in the failed repeal effort.

When it came to details, Trump "didn't know, didn't care, or both," one source had said.

It's possible that the chastening experience of health care reform's failure could prompt Trump to become more engaged on the tax issue. Given his long experience in business, the tax code is also closer to the President's area of expertise than the intricacies of the health insurance industry.

And, the urgency of the tax reform debate for Republicans could help to paper over cracks in the Republican coalition. GOP deficit hawks are now willing to embrace a plan that does not immediately pay for itself in order to get something done.

Rep. Mark Meadows, a fiscal conservative and member of the Freedom Caucus that helped scupper the leadership's Obamacare repeal plans, signaled flexibility over the tax plan Monday.

"We are perhaps at some short-term exposure on the deficit side of things," Meadows told CNN's Wolf Blitzer.

Building support

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But the White House has yet to solve the key impediments to building support for the tax plan. So far, outlines of the legislation suggest a fairly standard GOP tax bill that will ease the way for corporations and offer net advantages to the most wealthy in society -- an opening that Democrats are already exploiting.

Yet Trump's appeal during the campaign was anchored partially on his promise to be a champion of blue-collar voters in the Midwest and middle-class Republicans elsewhere.

That's one reason why the President shot down Monday a report that the ceiling on tax-free contributions to retirement plans could be drastically cut under the tax reform effort.

"There will be NO change to your 401(k). This has always been a great and popular middle class tax break that works, and it stays!" Trump tweeted Monday.

There will be NO change to your 401(k). This has always been a great and popular middle class tax break that works, and it stays! — Donald J. Trump (@realDonaldTrump) October 23, 2017

In another effort to show that the President was looking out for his core voters, his budget chief Mick Mulvaney told Fox News Sunday that Trump had repeatedly ruled out cuts to entitlement spending to pay for tax cuts.

Mulvaney said Trump told him: "I promised people I wouldn't change Social Security. I'm not going to do it."

In another possible sign that the White House is seeking to reconcile Trump's promises with traditional GOP tax policy , Axios reported that the plan could retain the current tax rate of 39.6% for those earning more than $1 million.

The move could partially dampen Democratic attacks that the tax plan represents a huge give-away to Trump and his rich friends, though it would disappoint traditional fiscal conservatives in the GOP.