Republican Sen. Ron JohnsonRonald (Ron) Harold JohnsonLiberal group launches campaign urging Republicans to support Biden's agenda Domestic extremists return to the Capitol GOP senator: Buying Treasury bonds 'foolish' amid standoff over debt ceiling, taxes 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 Mason ReidTo Build Back Better, we need a tax system where everyone pays their fair share Democrats say Biden must get more involved in budget fight Biden looks to climate to sell economic agenda MORE [(D-Nev.)] in the Senate, I think is next to impossible."

Several Republican senators, including Sens. Ted CruzRafael (Ted) Edward CruzMatthew McConaughey on potential political run: 'I'm measuring it' Professor tells Cruz that Texas's voter ID law is racist Schumer moves to break GOP blockade on Biden's State picks MORE (R-Texas), Mike LeeMichael (Mike) Shumway LeeThe Hill's 12:30 Report - Presented by Facebook - Dems attempt to tie government funding, Ida relief to debt limit Trump lawyer offered six-point plan for Pence to overturn election: book Graham found Trump election fraud arguments suitable for 'third grade': Woodward book MORE (R-Utah) and Marco RubioMarco Antonio RubioDemocrats face bleak outlook in Florida The Hill's 12:30 Report - Presented by Facebook - Dems attempt to tie government funding, Ida relief to debt limit Poll: Trump dominates 2024 Republican primary field 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 Ivan CantorBottom line Virginia GOP candidates for governor gear up for convention Cantor: 'Level of craziness' in Washington has increased 'on both sides' 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."