Republicans on Capitol Hill and beyond are worrying about the reverberations of the escalating feud between President Trump and Sen. Bob Corker (R-Tenn.).

The spat between the president and the chairman of the Senate Foreign Relations Committee has included Trump insulting Corker's height and accusing him of having "begged" for a presidential endorsement. The Tennessean has likened the White House to an "adult day care center."

At Tuesday's White House briefing, press secretary Sarah Huckabee Sanders ratcheted up the confrontation further, accusing Corker of having "rolled out the red carpet for the Iran deal." The president described the nuclear accord as an "embarrassment" during a speech to the United Nations General Assembly last month and could declare Iran to be noncompliant with the agreement soon.

Sanders also took a notably noncommittal stance when asked about a call from Trump's former chief strategist, Stephen Bannon, for Corker to "resign immediately."

Asked about the demand, which Bannon made during an interview with Fox News's Sean Hannity on Monday evening, Sanders said, "That's a decision for Sen. Corker and the people of Tennessee."

Corker aides take issue with the White House's characterization of his approach to the Iran deal, noting that he ultimately voted against the accord, which was reached during President Obama's time in the White House.

Republicans are perplexed by the vicious back-and-forth, which is coming at a time when Trump is already struggling mightily to make progress on his legislative agenda.

"There are not many Republican members of the Senate who have a lot of respect for the political skills of the president," said GOP strategist and pollster Whit Ayres, who includes Corker and Sen. Marco Rubio (R-Fla.) among his past clients.

Ayres acknowledged that the relationship between the White House and Senate Republicans was "strained."

Other more strident critics of Trump within the GOP noted that the president has already failed to keep Republican senators in line for crucial votes aimed at repealing and replacing the Affordable Care Act, also known as ObamaCare.

In that battle, Sens. John McCain (R-Ariz.), Lisa Murkowski (R-Alaska) and Susan Collins (R-Maine) proved impervious to White House pressure.

The main focus now is on tax reform. But no wide-ranging advance has been made on that topic since 1986, when Ronald Reagan was president, so success is far from guaranteed.

Many in the GOP believe his attacks on Corker are making a tricky climb even steeper.

"When you have a Congress so narrowly divided, [tax reform] is a monumental task, complicated by the president picking fights - and very bitter, personal fights - with people whose votes he has to have," said John Stipanovich, a veteran Florida-based GOP operative and Trump critic with ties to the Bush family.

"John McCain has a brain tumor. Bob Corker is retiring. Susan Collins is probably going to be governor of Maine," Stipanovich added. "They are not scared of Donald Trump!"

Some of Corker's views of Trump are widely shared by Republican power brokers in the capital, including other lawmakers, but they are normally expressed only in private. Publicly, senators have largely confined themselves to expressing a desire for the spat between the two men to end.

Sen. Chuck Grassley (R-Iowa) was asked about the furor on Monday and replied, "Both ought to cool it. Next question."

On Tuesday, Sen. Roy Blunt (R-Mo.) told CNN, "I'm supportive of both of them. I'd like to see it stop."

One aide to a GOP senator told The Hill of her boss, "I think as a general rule, the senator is not really interested in all the Twitter back-and-forth." This senator wanted "to keep the focus on legislation and moving forward, whatever the personal feelings," the aide added.

But the likelihood of the feud going away appears slight when it is the president himself who is upping the ante.

On Tuesday morning, Trump referred to the Tennessee senator as "Liddle' Bob Corker" and alleged that Corker was set up by The New York Times "to sound a fool."

In an interview with the Times on Sunday, Corker had suggested that Trump could lead the nation toward "World War III" and that his performance should "concern anyone who cares about our nation." He said that White House staff spent each day trying to "contain" the president.

Throughout the contretemps between Trump and Corker, some Republicans in Washington have expressed a weary lack of surprise.

"Trump is running an outside game working to appeal to his core base of support and doesn't necessarily care how this may or may not affect his relationship with the Senate," said Republican strategist Ron Bonjean.

"He has already set a precedent by publicly criticizing [Senate Majority Leader Mitch] McConnell and [Speaker Paul] Ryan, so it's not shocking that he will take on a chairman and try to make him a punching bag."

But the fear among many in the GOP is that Trump's eagerness to get into the fray ultimately hurts himself - and his party's agenda.

"I'm sure there are a lot of people who could play their roles more effectively," said Ayres. "But as Harry Truman said about the presidency: The buck stops here."

The Memo is a reported column by Niall Stanage, primarily focused on Donald Trump's presidency.