Sen. Lee in Obamacare Colloquy: 'Defund It Or Own It'

"All of these modifications have created additional uncertainty," Lee said.

"The president admitted this law is not ready for primetime… the American people deserve not to have this law implemented."

Lee took a jab at Republicans' strategy of figuring they could wait until Obama was defeated in 2012 to repeal the healthcare law. "That didn't happen," he noted.

Now, the Utah senator said, they need to wield "the power of the purse."

Sen. Rand Paul (R-Ky.), who wasn't in the Senate for the afternoon colloquy, said some Republicans' objection to taking the defund route is "like announcing preemptive surrender."

"Myself, Mike Lee, Ted Cruz, we're not arguing to shut down the government. We're arguing to defund Obamacare. But the Republicans that are announcing surrender, they have already taken the next leap. They are saying, oh, you want to shut down government. No, we don't," Paul said Monday on Fox.

"We are standing up for what we believe in and we want to use the leverage of the people who voted for us to try to get reform in government. I don't see how anybody could criticize that," he added.

House Speaker John Boehner (R-Ohio) said last week that votes in the lower chamber to defund parts of Obamacare had forced Obama to make changes to the law seven times "that would never have happened, had it not been for our continued efforts to defund this, and to repeal it."

"We will continue to do everything we can to defund it, to repeal it, and to make sure that the American people aren't put through this horrific experience," he said.

When asked about Lee's effort, though, Boehner said GOP leadership has "not made any decisions about how we're going to deal with the CR."

Coburn maintained, though, that the good intentions of the junior senators weren't anchored in reality.

"There is no way that the vast majority of funding can be stopped until you reverse the whole bill," he said.

On the question of state and federal health exchanges, CRS said in its report that "other sources of funding besides annual discretionary appropriations are available in FY 2014 and beyond to support exchange operations."

"ACA also provided the Secretary [of Health and Human Services] with an indefinite annual appropriation to award exchange planning and establishment grants to states through 2014," CRS continues. "Each year, the Secretary determines the amount of funding that will be made available to states through this grant program."

CRS didn't see the individual mandate being affected by current budget wrangling because the IRS wouldn't likely begin assessing the individual mandate penalties until 2015, for the 2014 tax year.

"If a government shutdown were to occur during calendar year 2014, the lapse in funding would not automatically suspend the requirements of the individual mandate," the report says. "In other words, during the time period that the government is shut down, taxpayers who fall within the coverage of the individual mandate would still be accruing penalties for any months in which they lacked minimum essential coverage."

Coburn said he'd be with Lee, Rubio and Cruz in voting against the continuing resolution. "I think that's terrible way to fund the government," he said.

Going the route of a replacement law is among their options, he said. "There wasn't any real debate on alternatives because we weren't allowed to offer them" back when the law was passed.

"We need to rein this president in, I agree," Coburn said. "If we could end [Obamacare], I'd end it tomorrow -- we need to delay to the point where we can kill it. It does need to be terminated."