Senate Republicans are rushing to distance themselves from President Trump's support for a fall shutdown.

Several GOP senators said Tuesday that they don't back shuttering the government in September even as the president endorsed the idea on Twitter during a series of early morning tweets.

"Obviously I disagree with that. No, I don't think there's a good government shutdown. ... Really it shows our inability to solve our nation's problems in a normal way," Sen. Bob CorkerBob CorkerA retreat from the Paris climate pact would imperil U.S. interests Cohn: US ‘probably looking to get tougher’ on Russia The Hill's 12:30 Report MORE (R-Tenn.), the chairman of the Senate Foreign Relations Committee, told reporters.

Sen. John McCainJohn McCainArmed Services chairman unveils .1B Asia-Pacific security bill Overnight Defense: Trump scolds NATO allies over spending | Flurry of leaks worries allies | Senators rip B Army 'debacle' | Lawmakers demand hearing on Saudi arms deal The case for protecting America's intelligence agency whistleblowers MORE (R-Ariz.) separately said there wasn't an appetite for a shutdown or changing the filibuster rules on legislation. Asked if Trump should stop tweeting, McCain responded, "I wish he would think twice before he tweeted."

Lawmakers face a Friday night deadline to avoid a government shutdown after passing a one-week funding extension. They will face a second deadline in the fall to pass the fiscal year 2018 bill or a short-term continuing resolution by Oct. 1 and avoid another potential shutdown.

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Republicans, who control the White House and hold a majority in both chambers of Congress for the first time in a decade, have been eager to show they can govern, with GOP leaders repeatedly downplaying the possibility that they will miss the funding deadlines.

Sen. John CornynJohn CornynRepublicans go to battle over pre-existing conditions Senate panel could pass new Russia sanctions this summer Senate staff to draft health bill during recess MORE (Texas), the Senate's No. 2 Republican, said on Tuesday that a shutdown would be an "abdication of responsibility, particularly if you're in the majority."

"Our voters, the people who elected Republican majorities in both Houses and elected this president, did not vote for us in order to shut down the government. They voted for us to govern, as hard as it is," Cornyn said from the Senate floor.

Sen. Jeff FlakeJeff FlakeLawmakers reintroduce measure to lift Cuba travel restrictions Majority of Senate supports Cuban tourism bill Montana GOP senator: Gianforte 'needs to apologize' MORE (Ariz.), who was a vocal GOP critic of Trump during his campaign, hit back at the president on Twitter, writing, "No, we don't need a government shutdown."

Sen. Lindsey GrahamLindsey GrahamSenate panel could pass new Russia sanctions this summer Overnight Cybersecurity: Bad Russian intel may have swayed Comey's handling of Clinton probe | Apple sees spike in data requests | More subpoenas for Flynn | DOJ's plan for data warrants Overnight Finance: GOP bill would leave 23M more uninsured, says CBO | Trump aides defend budget | Mnuchin asks for clean debt hike before August | Ryan says House could pass bill without border tax MORE (R-S.C.) said while he was "pretty much" a no on the omnibus funding bill, he didn't think a government shutdown was ever "good."

"The bottom line is, no, I don't want to shut the government down," he told CNN.

Trump sparked renewed talk about a fall funding fight Tuesday morning when he hinted in a series of tweets that he could have gotten a better funding deal if he didn't have to negotiate with Democrats, whose support is needed to pass most legislation through the Senate.

The president also pushed for nixing the Senate filibuster — a call also being rejected by GOP senators — and for a "good 'shutdown' in September to fix mess." 

either elect more Republican Senators in 2018 or change the rules now to 51%. Our country needs a good "shutdown" in September to fix mess!

— Donald J. Trump (@realDonaldTrump) May 2, 2017
White House budget chief Mick Mulvaney played defense over Trump's tweet Tuesday while telling reporters he wasn't worried about the September deadline.
 
"I think the president's tweet was that we might [want] a shutdown at some point to drive home that this place, that Washington needs to be fixed," Mulvaney said.
 
The Trump administration is expected to renew its push for U.S.-Mexico border wall funding in the fall bill. But top Democrats, including Senate Minority Leader Charles SchumerCharles SchumerHow Trump can score a big league bipartisan win on infrastructure Overnight Finance: Dems introduce minimum wage bill | Sanders clashes with Trump budget chief | Border tax proposal at death's door GOP senators distance themselves from House ObamaCare repeal bill MORE (N.Y.), are already predicting the administration won't be able to get the votes to get border legislation through the Senate, where he'll need Democratic support.
 
The government previously closed in 2013 for 16 days over a push by conservatives to use the funding bill to defund ObamaCare, a move that was considered a nonstarter by Democrats and the Obama administration.
 
Respondents to an ABC News/Washington Post poll conducted in October 2013 found that 53 percent of Americans blamed Republicans in Congress for the shutdown, compared to 29 percent who blamed then-President Obama.