Republican Sen. Ron JohnsonRon JohnsonOvernight Healthcare: Senate GOP to start writing its healthcare bill Senate staff to draft health bill during recess Divisions emerge in the Senate on pre-existing conditions MORE on Tuesday said it would be "next to impossible" to use a government funding bill to stop ObamaCare.

"Even if we were to not pass the continuing resolution [to fund the federal government], you're not going to be able to defund Obamacare, absent of President Obama signing a law, which I think is highly unlikely," the Wisconsin senator told the Milwaukee Journal Sentinel.

"So I appreciate the fact that they've raised the issue. But defunding Obamacare, with President Obama in the White House and Harry ReidHarry ReidGOP frustrated by slow pace of Trump staffing This week: Congress awaits Comey testimony Will Republicans grow a spine and restore democracy? MORE [(D-Nev.)] in the Senate, I think is next to impossible."

Several Republican senators, including Sens. Ted CruzTed CruzFEC faults Cruz on Goldman Sachs loans in rare unanimous vote CBO score underlines GOP tensions on ObamaCare repeal Republicans go to battle over pre-existing conditions MORE (R-Texas), Mike LeeMike LeeRepublicans go to battle over pre-existing conditions Senate gears up for fight on Trump's 0B Saudi Arabia arms sale Senate feels pressure for summer healthcare vote MORE (R-Utah) and Marco RubioMarco RubioSenate panel could pass new Russia sanctions this summer McConnell on Trump: 'We could do with a little less drama' Taking the easy layup: Why brain cancer patients depend on it MORE (R-Fla.), are putting pressure on GOP leaders to risk a government shutdown if Democrats don't agree to repeal the healthcare law.

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“If you fund this thing, you own it,” Lee said Tuesday on the "Sean Hannity" radio show.

“We cave and we cave and we cave,” he added. “This is how we get into trouble.”

But other top Republicans, including House Majority Leader Eric CantorEric CantorTrump nominates two new DOD officials Brat: New ObamaCare repeal bill has 'significant' changes Overnight Energy: Flint lawmaker pushes EPA for new lead rule MORE (R-Va.), have urged Republicans to abandon that hope, noting that there are not enough votes in the Senate.

"In order to avoid a government shutdown, we need 60 votes in the Senate and 218 votes in the House to pass a continuing resolution," Cantor told National Review's Robert Costa. "To get 60 votes in the Senate, you need at least 14 Democrats to join Republicans and pass a CR that defunds Obamacare. Right now, I am not aware of a single Democrat in the Senate who would join us. If and when defunding has 60 votes in the Senate, we will absolutely deliver more than 218 votes in the House."

At a press conference last week, President Obama said he assumed Republicans would not attempt to force the shutdown.

"The idea that you would shut down the government at a time when the recovery is getting some traction; where we’re growing, although not as fast as we need to; where the housing market is recovering, although not as fast as we would like; that we would precipitate another crisis here in Washington that no economist thinks is a good idea — I’m assuming that they will not take that path," Obama said.

"I have confidence that common sense, in the end, will prevail."