Sen. John Kennedy, R-La., said he wants to ban states from setting up a government-run healthcare system in a GOP bill to overhaul Obamacare that would allow states to set up their healthcare systems.

"I think a single-payer system is a bad idea," Kennedy said Monday. "I think if you give a big chunk of money to California they're going to go set up a single-payer system run by the state and then come back and say, 'We don't have enough money, we need more.' I think the only way we are going to solve the healthcare problem in America is through the private sector."

The GOP bill would divert funding from Obamacare to states in the form of block grants. It was introduced by GOP Sens. Lindsey Graham of South Carolina, Bill Cassidy of Louisiana, Dean Heller of Nevada and Ron Johnson of Wisconsin.

Kennedy defended his position to reporters who asked why he was in favor of handing decisions to states but not allowing them to set up a healthcare system funded and run by the state and federal government.

"I don't think states should have the authority to take money from the American taxpayer and set up a single-payer system," Kennedy said. "Some people think that's inconsistent with the idea of flexibility, but that's what the United States Congress is for. I very much believe in flexibility, and I know governors want flexibility, but it's our job to make sure that money is properly spent. I'm impressed by the fact that so many governors have signed on to this idea, on the other hand I've worked for two governors; you can generally get governors to sign on to things when you give them gobs of money."

Supporters of the Obamacare overhaul bill hope it can be passed through reconciliation, which requires just 50 votes to advance and pass in the Senate, assuming a tie-breaking vote by Vice President Pence. Republicans have a 52-seat majority, and Democrats have said they would vote against the overhaul. Sen. Rand Paul, R-Ky., has publicly opposed the bill because he said it keeps too much of Obamacare in place.

Some of Kennedy's other amendments include adding a work requirement to Medicaid, and providing more transparency around what medical procedures cost from facility to facility.

Asked how important the amendments were to gaining his support, Kennedy replied, "These amendments are important. I'm in the process of going through the bill."

The Senate faces a Sept. 30 deadline to use reconciliation, according to a recommendation from the Senate parliamentarian.

The sponsors behind the GOP bill haven't indicated that they oppose a single-payer plan from states. Graham, for instance, indicated during an interview with Breitbart over the weekend that he did not have any objection.

"If California wants to go down the single-payer road, knock yourself out," Graham said. "South Carolina is not going down that road. California can't take you with them."

When asked about the amendment, Cassidy called the idea of states setting up their own single-payer systems "impractical," and pointed out that other states, including Vermont and California, had tried to set up single-payer healthcare systems under Obamacare and had failed.

He said that under federal labor laws, states cannot confiscate dollars that employers put toward their workers' premiums, and said that was one of the reasons he didn't think that states could set up their own single-payer systems.

"There are some things that cannot be done ... You cannot do a single payer," he said. "It is a myth of the left because you have to confiscate all the money going to businesses ... Why do I have to address hypotheticals which are not possible?"

Robert King and Al Weaver contributed to this report