Sen. Lindsey Graham, R-S.C., explained how his healthcare idea would work during a presentation on the chamber floor Wednesday.

Graham and Sen. Bill Cassidy, R-La., introduced an amendment for the healthcare bill that would leave taxes on wealthy Americans in place and then transfer much of the power to the states when it comes to building a health insurance system.

"The model we have today is really disproportionate. It doesn't work, it's driving up healthcare costs all over the country. People are dropping coverage because the Obamacare mandates are too expensive," Graham said.

"So what we're doing is we're leaving the taxes on the wealthy in place. To my conservative friends: I'm sorry, but that's what we're gonna have to do to make this work."

Graham then explained that the medical device tax would go away, as would the individual and employer mandates.

"We're able to take that money [from taxes], plus money we would give to insurance companies to stabilize the national market, and block grant it back to the states with a formula that's fairer."

Graham has touted his healthcare idea with several media outlets in the last few weeks as the debate about how to to fix the nation's healthcare system rages on.

The Senate voted down a simple repeal of Obamacare in a Wednesday vote.