Senate Republican leaders are mulling the idea of returning to the Obamacare repeal effort and hold a vote on a bill that would repeal the healthcare law's structure and replace it with block grants to states and roll back the Medicaid expansion.

The bill, proposed by Sens. Lindsey Graham, R-South Carolina and Bill Cassidy, R-Louisiana, would need 51 votes to pass under the budget reconciliation process. Due to a ruling by the Senate parliamentarian, Senate Republicans have only until the end of the month to use the obscure procedure.

GOP leaders have not yet made a final decision, reports Politico, which said that it would be brought to the floor if 50 of the 52 Republican senators express support for it.

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Despite the renewed effort, it will be a steep uphill climb for Republicans. The Congressional Budget Office (CBO) has not scored the measure yet and it already faces likely opposition from at least Sen. Rand Paul, R-Kentucky, and potentially moderates like Sen. Susan Collins, R-Maine.

Sen. John McCain, R-Arizona, who supports the measure, seems reluctant to commit to pushing it through right now, telling CBS's "Face the Nation" on Sunday that he wants to see it go through the committee process instead.

"Are we going to ram through our proposal with, with Democrats and the president? That's not the way to do it. We got to go back. If I could just say again, the way to do this is have a bill, put it through the committee," said McCain, who was one of the three senators who voted against the final repeal effort at the end of July.

Even if the Senate were to pass Graham-Cassidy, the House would have to take it up and pass it with no changes.

CBS News' Nancy Cordes contributed to this report.