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 CorkerRobert (Bob) Phillips CorkerDeficit hawks voice worry over direction of tax plan The Hill Interview: Budget Chair Black sticks around for now Overnight Finance: White House requests B for disaster relief | Ex-Equifax chief grilled over stock sales | House panel approves B for border wall | Tax plan puts swing-state Republicans in tough spot MORE (R-Tenn.), the chairman of the Senate Foreign Relations Committee, told reporters.

Sen. John McCainJohn Sidney McCainRubio asks Army to kick out West Point grad with pro-communist posts The VA's woes cannot be pinned on any singular administration Overnight Defense: Mattis offers support for Iran deal | McCain blocks nominees over Afghanistan strategy | Trump, Tillerson spilt raises new questions about N. Korea policy 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 CornynGun proposal picks up GOP support House bill set to reignite debate on warrantless surveillance Republicans jockey for position on immigration 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 FlakeJeffrey (Jeff) Lane FlakeAuthorizing military force is necessary, but insufficient Republicans jockey for position on immigration McCain, Flake warn against 'politically-motivated penalties' for Canadian defense firm 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 Olin GrahamDurbin: I had 'nothing to do' with Curbelo snub Republicans jockey for position on immigration Overnight Health Care: House passes 20-week abortion ban | GOP gives ground over ObamaCare fix | Price exit sets off speculation over replacement 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 (Chuck) Ellis SchumerOvernight Health Care: Schumer calls for tying ObamaCare fix to children's health insurance | Puerto Rico's water woes worsen | Dems plead for nursing home residents' right to sue Crying on TV doesn't qualify Kimmel to set nation's gun agenda Trump knocks ‘fake’ news coverage of his trip to Puerto Rico 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.