Donald Trump made his first visit as president to the Senate on Tuesday, trying to unite his party around tax reform at a lunch with Senate Republicans. Nothing unusual there. Presidents in the past have rolled down Pennsylvania Avenue to rally support for a top priority.

What dropped jaws was what came before and after the lunch – a remarkable public display of criticism and concern about the country under President Trump voiced by senators in his own party: Bob Corker (R) of Tennessee and Jeff Flake (R) of Arizona. The Arizonan announced Tuesday afternoon he will not seek reelection, laying out as a “matter of duty and conscience” his concerns about the president, his party, and the country.

Both men have been targets of searing tweets from Mr. Trump. Indeed the day began with a tweet assault on Senator Corker, chairman of the Senate Foreign Relations Committee, who later attended the lunch. Corker had been on early-morning television, essentially telling Trump to let Congress work its will on taxes and butt out.

That touched off a twitter blast from Trump, taunting Corker that he “couldn't get elected dog catcher in Tennessee.” The senator recently announced he would not run for reelection. When CNN caught up with Corker, he unloaded on the president, accusing Trump of “constant non-truth telling,” saying he would not vote for him now, that he was no role model for children, and that the president would be most remembered for “the debasement of our nation.”

It was not their first duel, and intense feuds between presidents and members of their own party are not unique in history, says political historian Julian Zelizer, of Princeton University. Lyndon Johnson famously hated Robert Kennedy; George H.W. Bush battled with Newt Gingrich.

The difference, says Professor Zelizer in an email, is the kind of rhetoric the current president uses, the apparently ad-hoc and very public ways in which he voices his scorn, “and the incredibly poor timing of doing this at the exact moment he needs support on the Hill.”

Unlike other cases, “Trump has almost no legislative victory, incredibly thin support, and so the risks of his doing this are immense,” writes Zelizer.

That is not how many Republicans see it, however.

Before Senator Flake’s stunning announcement, House and Senate Republican leaders batted away the reignited feud with Corker as a distraction that won’t affect the agenda at hand. Republican senators described Trump’s lunch as upbeat, with the president saying he had their back. He encouraged them on tax reform, deregulation, and said to keep working on health care, senators at the meeting said. Corker told reporters that the grenade tosses of the morning did not come up.

“There is a lot of noise out there,” Senate majority leader Mitch McConnell said in response to a reporter’s question after the luncheon. But what Republicans “are concentrated on is the agenda of the American people.” He described “great cohesion” on getting taxes done before the end of the year.

Indeed, tax reform is the holy grail of the GOP, and its centrifugal forces can be felt in both houses.

'It's all nonsense.'

“Who cares?” asks John Feehery, commenting on the Trump-Corker outburst of the morning. Mr. Feehery, who was the spokesman to former Rep. Dennis Hastert of Illinois when he was speaker of the House during the presidency of George W. Bush, said it’s now well known that Trump likes to fight back and that tweets are irrelevant to the tax debate.

“The House will pass this thing. I don’t think Bob Corker will vote one way or the other given that the president insulted him. It’s all nonsense.” Indeed, Corker told the Monitor after the meeting that his vote will be independent of what the White House says. He has been a critic of a tax plan that would add to the national debt, which now tops $20 trillion.

Despite his rocky relations with several GOP senators, the president has better relations with Republicans in the House, particularly with hardliners. In the past, they bucked House leaders, partially shutting down the government in 2013 over the budget and the Affordable Care Act, and then pushing House Speaker John Boehner (R) of Ohio from the speakership – and office.

Last spring, Trump was able to corral the House’s jumping frogs, as Speaker Boehner used to characterize his caucus, to back a GOP health-care plan that didn’t fully repeal Obamacare.

And in a recent conference call with House Republicans, he seemed to convince members – many of them deficit hawks – that they should adopt the Senate’s debt-busting budget, because it was their best chance at tax reform.

“He was very constructive in trying to get this budget done,” says Feehery, adding that the president should be credited for squashing a recently floated idea to change the way people contribute to their 401(k) retirement plans. “It was a stupid idea, alienating his whole political base.”

Learning curve on the Senate

But the Senate is another matter. The 100 individuals there wield more power, represent far more diverse constituencies, and work under rules that aim to forge consensus – or end in gridlock. The president has criticized majority leader McConnell for not being able to deliver on health care, even while the leader enjoys support from his caucus. They know how tough it is to deliver on anything when Republicans hold the majority by a margin of only 2 seats.

“Trump hasn’t really come to understand the Senate as an institution, the rules, the procedures, the history, and what can be successful there,” says Matt Mackowiak, a GOP consultant in Texas and a former senior Senate aide. “McConnell does understand that.”

That’s why the Republican Senate leadership is concerned about efforts by Trump’s former strategic adviser, Steve Bannon of Breitbart News, to challenge incumbent GOP senators up for reelection – Flake among them.

Before this afternoon, that is.

In announcing that he will not run, Flake said it is clear that a “traditional Republican” has a “narrower and narrower path to nomination.” The party, he said, had given up on its core principles in favor of a “more viscerally satisfying anger and resentment.”

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Those feelings are justified, “given the royal mess that we’ve created,” he admitted. However, he concluded, “anger and resentment are not [a] governing philosophy.”

David Sloan contributed to this report from Washington.