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WASHINGTON President Donald Trump's stepped-up attacks against Senate Republicans are threatening the fall's busy legislative agenda and any cooperation that remains between them.

In a raucous speech Tuesday night followed up by Wednesday morning tweets, Trump endorsed a government shutdown, criticized both of the state's GOP senators, called out Majority Leader Mitch McConnell by name and once again called for drastic changes to the rules governing the upper chamber of Congress.

By Wednesday evening, however, the White House put out a statement that said Trump and McConnell "remain united on many shared priorities, "including middle class tax relief, strengthening the military, constructing a southern border wall, and other important issues." The statement also promised the two would hold previously scheduled meetings this month.

But the onslaught of criticism continues to erode a relationship between Senate Republicans and the White House that has grown more tense in recent weeks, especially after a series of failures on health care reform. And the president took out his frustration in front of a crowd of supporters in Phoenix Tuesday.

Reviving one of his biggest campaign promises, Trump pressed Congress to build a wall on the nation's southern border, threatening to shut down the government if Congress doesnt move forward.

Build that wall," he demanded. "The obstructionist Democrats would like us not to do it. But believe me, if we have to close down our government, we're building that wall, Trump said.

The House of Representatives has approved a down payment of $1.6 billion for a wall while the Senate hasnt committed to such an expenditure.

Trumps statement is setting up another intra-party fight with Republican senators just as a Sept. 30 deadline is quickly approaching to continue funding the government. Even though a shutdown appears unlikely with the party in control of both chambers of Congress and the White House, Republicans believe they would suffer severe repercussions at the ballot box in 2018 if the government were forced to close its doors.

In a move likely to further strain what is supposed to be a partnership with the Senate majority leader, Trump also called out McConnell by name as a way to pressure him into changing Senate rules so that passing legislation would require the support of just 51 senators instead of 60.

We have to get rid of what's called the filibuster rule; we have to. And if we don't, the Republicans will never get anything passed. You're wasting your time, Trump said. And we have to speak to Mitch and we have to speak to everybody.

Trump followed up with a tweet Wednesday morning.

But McConnell has no plans to change the Senate rules. Even if he wanted to, he would need the support of 50 senators.

Theres not a single senator in the majority who thinks we ought to change the legislative filibuster. Not one, he told reporters in April, a position that hasnt changed.

Trumps focus on changing Senate rules and building the border wall is out of line with what Republicans want to accomplish. They are facing a busy fall in which they must raise the debt limit to allow the U.S. government to pay its bills, and to pass vital legislation like reauthorizing the childrens health insurance program. Theyd also like to accomplish tax reform, but Trump didnt mention any of these priorities at his rally.

Hes got the best pulpit out there and he understands the importance of messaging, said Billy Piper, former chief of staff to McConnell. Piper said the president "ought to be talking about" moderate Democratic senators like Joe Donnelly, D-Ind., Heidi Heitkamp, D-N.D., and Claire McCaskill, D-Mo., "and the need to get them on board with tax reform.

Instead of pressuring Democrats, Trump appears to be focused on the shortcomings of his own party after months of bubbling tensions.

Trump was not supportive of sanctions Congress overwhelmingly passed against Russia earlier this summer, even though he did sign them into law.He has publicly attacked McConnell, suggesting he should step down as leader and blaming him for the failure of health care legislation. And the two had at least one contentious phone conversation in early August that resulted in Trump lobbing additional attacks on the majority leader.

And Senate Republicans have been expressing their own frustration more openly in recent weeks. After Trump's defense of some of the white nationalist protesters in Charlottesville, some members of the party stepped up their criticism. Sen. Bob Corker, R-Tenn., said that Trump doesn't have the "stability nor some of the competence" necessary for the job.

In public, Republican leaders have tried to downplay any challenges with Trump. The President and I, and our teams, have been and continue to be in regular contact about our shared goals, McConnell said in a statement Wednesday afternoon. We have a lot of work ahead of us, and we are committed to advancing our shared agenda together and anyone who suggests otherwise is clearly not part of the conversation."

And House Speaker Paul Ryan dismissed the idea of a shutdown.

I don't think a government shutdown is necessary and I don't think most people want to see a government shutdown, ourselves included, Ryan told reporters in Hillsboro, Oregon.

Theres no desire to get into it with Trump, Piper said of congressional Republicans.

But the president's criticisms continue. He attacked Arizona Senators John McCain and Jeff Flake in their home state Tuesday night despite admitting that Republicans asked him not to criticize members of his own party.

Flake refused to respond to Trump's attacks on Fox Radio's Brian Kilmeade show Wednesday, saying, "I saw that part where he talked obviously about me and about Sen. McCain and you know Im just focused on working for the state doing my day job."

Steven Law, a former chief of staff to McConnell and current CEO of the Senate Leadership Fund, a super PAC endorsed by McConnell to elect Senate Republicans, said that Republicans will be hyper-focused not on Trump but on tax reform in the fall.

"The president needs to make up his own mind on how to invest his political capital," Law said.

Read more:
Trump's Continued Attacks On Senate Republicans Hamper Party's Agenda - NBCNews.com