Last week, House Republicans passed a continuing resolution that would fund the government through mid-December while stripping money for ObamaCare. Lee said the House listened to “what the American people have demanded” by trying to defund ObamaCare.

Senate Majority Leader Harry ReidHarry ReidWeek ahead: House to revive Yucca Mountain fight Warren builds her brand with 2020 down the road 'Tuesday Group' turncoats must use recess to regroup on ObamaCare MORE (D-Nev.) is expected to advance the House spending bill while stripping out the language that defunds ObamaCare. Lee said that would be unacceptable. He said the Senate should either hold an up-or-down vote on the House measure as is, or allow a completely open amendment process.

The government will shut down on Oct. 1 if Congress doesn't approve some form of government funding measure. 

Lee, along with Sen. Ted CruzTed CruzWeek ahead in tech: Trump's antitrust pick heads before Senate Week ahead: Senate panel to vote on Trump's FDA pick Warren builds her brand with 2020 down the road MORE (R-Texas), has been a vocal critic of the healthcare law and has said this is the best opportunity Republicans have to stop its implementation.

Republicans have argued that the Affordable Care Act, also known as ObamaCare, harms the economy and increases unemployment because of business mandates under the law.

“If the administration goes ahead with this law anyway, we know that ObamaCare will be implemented in a way that is manifestly unfair,” Lee said. “We know that the law is unaffordable and we know it’s going to be bad for the economy.”

Democrats point out that the law is already benefiting those with preexisting conditions who can’t be denied coverage, people younger than 26 who can stay on a parent’s insurance plan and women who now pay less for preventive healthcare.