They've said it could include provisions continuing federal payments to insurers that help them contain costs for some low earners and inducements to keep healthy people buying policies - a step that helps curb premiums.
When asked if he has had any conversations with McConnell about the bill since lawmakers left Washington for a holiday break, Paul was curt.
I'm concerned about the health bill that may be brought to the Senate for vote.
Meanwhile, minority leader Chuck Schumer expressed encouragement on behalf of Democrats.
"We have to get more consumer decision-making involvement in the process and more transparency", he said.
VIDEO: Tell your Senators to oppose the Senate healthcare bill. "Does anybody remember us complaining that Obamacare had insurance bailouts?" The independent Congressional Budget Office analysis reports that the Republican bill would leave 22 million uninsured and millions left besieged because of the almost $800 billion in proposed Medicaid cuts. Or will they vote because their political leaders tell them what to do?
"The Consumer Freedom Option simply says that if an insurance company sells in a given state a plan that is consistent with the Title I mandates, that company can also sell any other insurance plan consumers desire". They will understand that these members were relying on President Obama to veto their efforts - some Republicans never really wanted to have their bills become law. Under "Obamacare", the CBO found, he'd pay $1,700 in premiums. The House and Senate GOP have excluded Democrats from their secretive closed meetings that have resulted in such flawed health care alternatives. "I'm not for that, but I'm saying, I want repeal to work, and the way you do it is you separate into two bills and you do it concurrently". "There are a lot of moving parts".
The Senate version of the bill, the Better Care Reconciliation Act, would eliminate the ACA's requirement that people prove they have health coverage, would repeal or delay billions in taxes imposed under the current law, and would make long-term deep cuts to the nation's Medicaid program.
Trump has also previously suggested that he was open to working with Democrats to fix the health care system, but last week endorsed the controversial measure that would repeal Obamacare outright without a replacement at the ready.
Sen. Ted Cruz, R-Texas, said Thursday on San Antonio's KTSA Radio that the GOP's Senate majority "is so narrow, I don't know if we can get it done or not".
Other conservative groups like the amendment. "We're gonna see what we can do, we're getting very close", President Donald Trump said last week, shortly after McConnell announced that the Senate would take the July Fourth recess to find a new way forward.