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The bill is being pushed through the Senate using the reconciliation process, which allows Republicans to bypass a filibuster and pass the legislation with a simple majority. In a Senate where Republicans have only a two-vote majority, any defectors can derail the process like they did during the last attempt in July.
Louisiana Sen. Bill Cassidy, who is one of the bill's co-authors, said he could not determine the current vote count or whether it was likely to pass.
"I'm still cautiously optimistic but there's a lot of moving parts." said Sen. Ron Johnson of Wisconsin, another one of the bill's architects. "It's kind of coming together."
Arizona Sen. John McCain, who was one of the deciding votes against the previous Obamacare repeal effort, told reporters he is undecided on the bill. McCain said that while he is not waiting for an official analysis from the nonpartisan Congressional Budget Office, he wants the bill to be passed through regular order.
"I am going to continue to look at this as the process goes on," McCain said. "I want a regular order and that's what I said a week ago - two weeks ago."
While a handful of moderate Republicans are still mulling their support, the only vocal GOP senator to come out strongly against the bill is Rand Paul of Kentucky.
"You know I'll do everything I can to describe this as keeping Obamacare, Obamacare lite," Paul said. "But I oppose it and we'll see what happens."
Meanwhile, Senate Democrats are left on the sidelines as Republicans whip the votes in their own conference. Through the reconciliation process, they do not have much, if any, options to block the bill.
However, Senate Minority Leader Chuck Schumer said in a press conference earlier Monday that he is exploring any and all ways his conference can prevent the Graham-Cassidy bill from passing.
"Look, this is so outrageous and so harmful that we're going to look at every possible way to slow this bill down," Schumer said.
One of the things Schumer wants to do is get a concrete score from the Congressional Budget Office, which he believes would shine a light on the ramifications of the bill if it were to become law.
"It would be outrageous for our Republican colleagues to vote for this bill without knowing its effect on people," Schumer added. "That - whatever your ideology - would be nothing short of a disgrace."
But the CBO announced in a statement Monday that it will only be able to provide a preliminary score of the bill, without any "point estimates of the effects on the deficit, health insurance coverage, or premiums for at least several weeks."