Speaking to reporters in the Capitol, Sen. John Cornyn of Texas said there has already been a great deal of House and Senate negotiating and he considers the GOP-introduced bill Monday a product of the House and Senate.
"Probably straight to the floor," Cornyn said when asked by CNN about the process. "Because there has already been a lot of consultations on a bicameral basis to get us here."
The process Cornyn outlined, which leaders have not formally announced, is in keeping with comments by Senate Majority Leader McConnell who Tuesday hinted he might move the bill quickly to he floor.
"I encourage every member to review it because I hope to call it up when we receive it from the House," McConnell said.
A Senate GOP aide acknowledged the plan could cause some unhappiness among Republicans seeking to shape the bill in committee and open leaders up to charges they are trying to ram the measure through Congress with little time for review.
Freshman Republican Sen. Bill Cassidy of Louisiana said he would prefer to have the health law rewrite be considered by the Senate committees where it could be shaped by the chamber's health policy experts but said it was a decision for the leadership to make and he would accept it.
"That's a decision for others to make," he said.
Cornyn acknowledged that getting Republicans to stick together to get the 51 votes needed to pass the bill is "critical because Democrats aren't going to help at all."
"That's a conversation we are going to have (Tuesday) at lunch and continue until we get it across the finish line," he said as he entered a lunch also attended by Vice President Mike Pence and Health and Human Services Secretary Tom Price to discuss the health care law.
On the tricky and and complicated question of whether the bill will meet the technical rules of reconciliation in the Senate, Cornyn expressed confidence the bill will pass muster with the Senate Parliamentarian who will be the sole judge of that.
"We've been consulting with the parliamentarian off and on the whole time," Cornyn said.