Republicans would never do that sort of back-room negotiating of a bill of this scope, Graham said.
"We're not going to put the whole nation at risk and take a broken system and make it worse just to get a vote," Graham said. "No way in hell."
"This process is not legislation. This process is corruption," said Sen. Tom Coburn, R-Okla. "It is a shame that the only way we can pass this legislation is to buy votes."
McConnell said Republicans will insist on using all their parliamentary time even after that vote, when it is clear that the bill will pass. If Republicans insist on all their time for debate, a vote on final passage of the bill is likely to occur at 7 p.m. on Christmas Eve.
"People have to show up and vote at least three more times," McConnell said, arguing that time is good for the process as lawmakers and the public read through the bill.
The Congressional Budget Office updated its cost estimate Sunday, guessing that deficit reduction under the bill could actually be half of the more than $1 trillion forecast between 2020 and 2029.
"This is not over, by any stretch," McConnell said.
If Senate Democrats pass their bill later this week as they seem sure to do, the next step will be a post-holiday conference to reconcile the House and Senate versions. Given the real differences between the two, that may not be easy.
The House version includes a public health insurance option, while the Senate version would follow the model of insurance for federal workers, allowing insurers to create national health plans overseen by a federal agency.
There are also differences in how the legislation is paid for: The House taxes wealthy Americans, while the Senate would, among other revenue measures, tax high-cost insurance plans. Unions oppose that measure.
But those fights, assuming Democrats can maintain perfect attendance this week, will wait for after the holiday.