Senate Majority Leader Mitch McConnell is set to sit down with President Donald Trump Monday in a White House meeting that could help patch their relationship, which fractured in a big way over the summer, when the two leaders took shots at each other over health care reform and the effectiveness of Congress.

Back in August, Trump said he was “very disappointed in Mitch,” after McConnell said Trump had “excessive expectations” about the legislative process.

The meeting comes as conservative groups demand McConnell step down from his leadership role.

“We call on all five members of the GOP Senate leadership to step down, or for their caucus to remove them as soon as possible,” Ken Cuccinelli, the former attorney general of Virginia who now leads the Senate Conservatives Fund, said Wednesday on Capitol Hill.

McConnell “will join the President and Vice President for a working lunch where they will discuss the fall agenda which includes completing the budget resolution, passing tax reform to help American families and workers, confirming well-qualified judicial and other nominees, and continuing to provide resources to communities affected by the recent hurricanes,” the Senate GOP leader's spokesman David Popp told Fox News.

Steve Bannon, former chief strategist to Trump, said Saturday in a speech to religious conservatives that he’s committed to dumping McConnell.

Bannon put on notice some of those incumbents who are at risk of a challenge from his flank of the party. He said lawmakers possibly can avoid that wrath if they disavow McConnell and meet other conditions.

"This is our war," Bannon said. "The establishment started it. ... You all are gonna finish it."

But Sen. Lindsey Graham, R-S.C., said, “Mitch McConnell’s not our problem. Our problem is that we promised to repeal and replace ObamaCare, and we failed. We promised to cut taxes and we have yet to do it.”

The senator added: "If we're successful, Mitch McConnell's fine. If we're not, we're all in trouble. We lose our majority and I think President Trump will not get reelected."

Sen. Susan Collins, a moderate from Maine who was a critical “no” vote on health care, said Bannon’s rhetoric is what Americans are tired of.

"They don't want this hyperpartisanship. They want us to work together. And they want us to get things done," she said.

Collins added that "over-the-top rhetoric is not helpful. Mitch McConnell is the Senate majority leader. The president needs him. I'm glad they're working together on tax reform and a lot of other issues. And I'm glad they're meeting this week."

In August, Trump tweeted blame for failure to repeal ObamaCare on McConnell, saying, “Can you believe that Mitch McConnell, who has screamed Repeal & Replace for 7 years, couldn’t get it done. Must Repeal & Replace ObamaCare!”

McConnell responded to Trump’s Twitter barrage by saying the challenges of governing shouldn’t be a surprise.

"A lot of people look at all that and find it frustrating, messy. Well, welcome to the democratic process. That's the way it is in our country," McConnell said at a GOP event in Kentucky this summer.

Meanwhile, the senators’ weeklong recess also drew criticism from the White House.

"They're on another vacation right now. I think that we would all be a lot better off if the Senate would stop taking vacations, and start staying here until we actually get some real things accomplished," Press Secretary Sarah Sanders said.

Recently, a McConnell-backed political committee spent millions and Trump endorsed Alabama Sen. Luther Strange in a recent primary election, but Bannon-backed Roy Moore prevailed. Moore, a former judge, has defied federal court orders, described Islam as a false religion and called homosexuality evil.

Senate Republicans had been upbeat about adding to their 52-48 edge in the chamber, especially with Democrats defending more seats next year — 10 in states Trump won in last year's presidential election. But the Bannon challenge could cost them, leaving incumbents on the losing end in primaries or GOP candidates roughed up for the general election.

"If we don't cut taxes and we don't eventually repeal and replace ObamaCare, then we're going to lose across the board in the House in 2018. And all of my colleagues running in primaries in 2018 will probably get beat. It will be the end of Mitch McConnell as we know it. So this is a symptom of a greater problem," Graham said.

He added that Bannon "can't beat us if we're successful. And if we're not successful, it doesn't matter who tries to beat us, they'll be successful."

Fox News' Mike Emanuel and The Associated Press contributed to this report.