"Here is what will happen," Graham said in an exclusive interview with CNN's Kate Bolduan. "If you like Obamacare, you can re-impose the mandates at the state level. You can repair Obamacare if you think it needs to be repaired. You can replace it if you think it needs to be replaced. It'll be up to the governors. They've got a better handle on it than any bureaucrat in Washington."
Cassidy, who is a physician, explained that the plan would keep popular protections under Obamacare, including a ban on denying coverage for pre-existing conditions.
"The essential health benefits will still be there. We can't repeal those as part of the process and so you'd still have the protection. This perfectly fulfills the Jimmy Kimmel test," Cassidy explained, referring to the exchange he had earlier this year with Kimmel after the late night host made an emotional plea about protecting people with pre-existing conditions
like his newborn son, who was born with congenital heart disease.
Graham and Cassidy, who have been working closely with former Pennsylvania Republican Sen. Rick Santorum, argue that one of the main reasons that Republicans are having such a hard time agreeing is because they are working from the Obamacare template -- particularly federal control of health insurance.
"The reason we can't pass a bill is because we are trying to do it in Washington, so stop it," Santorum, a CNN contributor, told CNN. Both senators agree that the key to making their plan work, is giving states flexibility. "A blue state can do a blue thing, a red state a red thing," Cassidy said. "My state is going to repeal and replace Obamacare with something that gives power to the patient, but that starts with us giving power to the states."
Additionally, the version of the Republican bill first unveiled last month has turned out to be a tough sell back home because it repeals Obamacare taxes, effectively giving wealthier Americans a tax cut, while also making cuts to Medicaid, which now helps many afford health insurance.
At the same time that Graham is unveiling his plan, GOP Senate leaders released publicly a new version
of their proposal Thursday morning.
Graham and Cassidy explained that they are not trying to undermine Senate Majority Leader Mitch McConnell's effort.
"We're going to support Mitch's effort with his new plan, but we want an alternative and we're going to see which one can get 50 votes," Graham said. "We're not undercutting Mitch, he's not undercutting us."
Graham told CNN that he believes their new idea would address the problems found in the original bill.
First, it would maintain taxes on wealthy Americans put in place by Obamacare, taxes intended to help pay for insurance subsidies. That revenue, which they estimate to be about $500 billion, would be sent to the states.They are still waiting to see a score from the Congressional Budget Office to confirm that figure.
"We're leaving in place the taxes on the wealthy, taking that money and giving it back to the governors to come up with better healthcare," Graham said.
The senators did point out that even though the plan keeps those taxes in place for now, they may eventually be repealed as part of changes to the tax code. "It may be that those taxes that are being kept will be eventually repealed, but it will be done as part of comprehensive tax reform, not as part of this," said Cassidy. "Our problem has been trying to combine tax reform with replacement of Obamacare. Putting those two together has not worked."
The Obamacare tax levied on medical device makers would be repealed, as would the mandates for individuals to have insurance and for employers to provide affordable coverage. Graham and Santorum say that would amount to about $220 billion in revenue cuts. Graham and Santorum argue those tax penalties not only funded the Affordable Care Act mandate conservatives despise, but they also ended up hitting working people.
The idea is modeled on the Welfare Reform Act of 1996, which dismantled the federal entitlement program with block grants to the states.
That, however, was done in a bipartisan way -- with GOP leaders like Santorum working with then-President Bill Clinton.
For the latest health care discussions, no Democrats have signed onto the legislation and it is unlikely many, if any, would even vote for such an idea.
Instead, the name of the game is finding elusive consensus just among Republicans -- and even that may not be possible.
Graham and Santorum say the key to getting traction on their idea is buy-in from GOP governors, some of whom have significant influence with their Republican senators.
One of the aspects of this proposal would be to include so-called "inflators" -- which would allow states that find formulas for quality, affordable health care to keep the federal dollars they save by doing so. The amount of money each state gets will be based by region.
"It will be a state block grant, not an individual entitlement, and each state will be treated fairly," Graham said. "The more efficient you are, the more money you'll have."
Graham and Santorum both say they have been talking to one another seriously about this idea for months, but when the Senate GOP bill began to falter at the end of June, they kicked it into high gear.
Santorum went to the White House last week to discuss the idea with senior aides to President Donald Trump, and he and Graham have been lobbying Senate colleagues, seeking input.
This story has been updated and will update as news develops.