Lee has persuaded 11 of his colleagues to sign on to his plan to reject any bill that would fund the government past Sept. 31 unless it is devoid of funding for Obamacare. If he were to be successful, the health care law would be delayed for roughly a year. As it stands, Obamacare is expected to go into full effect on Jan. 1.
"Maybe we can't repeal it right now, but we can delay its funding and if we delay its funding we can stop its consequences for now," he said. "There were many of us elected specifically with this mandate in mind that we have to stop this law."
To implement his plan, Lee would need 41 Republicans and even if he got them, that doesn't mean President Barack Obama would agree to delay implementing his signature domestic achievement to avoid a shutdown.
Many Republicans, such as Sens. Orrin Hatch, R-Utah, and Richard Burr, R-N.C., believe this tactic has almost no chance of success but would allow Democrats to paint Republicans as obstructionists. Burr was the one who called Lee's attempt "the dumbest idea I've heard."
Rep. Tom Cole, R-Okla., said it was the political equivalent of a "temper tantrum." So far, about 60 of Cole's GOP colleagues in the House have signed on to the effort.
Lee believes that Democrats would back down and that a shutdown would never occur.
"We all know the government is going to get funded, the only question is whether it is going to get funded with Obamacare or without it," he said.
Lee's argument is that Obama is selectively enforcing the health reform law, already delaying a mandate that big employers offer insurance or pay a fine and a requirement that individuals demonstrate their financial situation before receiving a subsidy to pay for insurance.
"If the law is not ready for prime time, then Congress shouldn't fund it," he said.
On Oct. 1, the government will start enrolling individuals into insurance plans through new exchanges, online insurance marketplaces. And after Jan. 1, almost every American must demonstrate that they have insurance or pay a fine through their taxes.