The bill would also gradually increase the Medicare-eligibility age, which is now 65, by three months a year until it reaches 70.
"It is moving a system that is troubled and that faces really difficult times ahead and puts it on a path toward some sort of sustainability," said Lee.
Paul estimated his legislation would save $1 trillion in a decade.
Changes to the financially troubled Medicare system have proven to be not only politically difficult but also easy for the parties to use as a weapon in election years. For example, Republicans used fears about the new health reform law's impact on Medicare in the 2010 election cycle and Democrats repeatedly ripped a House Republican plan that would privatize Medicare last year.
House Democrats sent an email to reporters criticizing Paul's plan on Thursday that said: "Seniors want the Medicare program they know and rely upon to be strengthened and protected not dismantled."
DeMint predicted the Democratic response and said the group took steps to minimize such complaints by linking it to the insurance members of Congress now receive.
"I'm sure our Democrat friends will distort what they in fact have suggested including Barack Obama that we need to give seniors what we give congressmen," DeMint said.