Senate Majority Leader Mitch McConnell has asked the Congressional Budget Office to quickly score an Obamacare overhaul bill introduced this week, his office confirmed Friday.

The bill would take revenues from Obamacare and distribute them as block grants to states so they could write their own healthcare plans. Sen. Bill Cassidy, R-La., introduced the bill along with Sens. Lindsey Graham of South Carolina, Dean Heller of Nevada, and Ron Johnson of Wisconsin.

A CBO score would make projections about government spending and include information about whether people will lose or gain health insurance coverage.

Supporters hope the bill can be passed through reconciliation, which would require just 50 votes to advance and pass in the Senate, assuming a tie-breaking vote by Vice President Pence. Reconciliation is a budget measure that allows passage with a simple majority rather than the 60 votes needed to block a filibuster. The Senate faces a Sept. 30 deadline to use reconciliation, according to the Senate parliamentarian.

Cassidy said the bill has support from 48 or 49 GOP senators, though many have not publicly stated where they stand. Sen. Rand Paul, R-Ky., announced he would not be in favor of the legislation, which he called "Obamacare lite."

The last time the Senate tried to narrowly repeal Obamacare through reconciliation, in July, it failed by one vote, unexpectedly cast by Sen. John McCain, R-Ariz. The other Republican senators who voted against the measure, which would have narrowly repealed provisions in the law, were Sens. Susan Collins of Maine and Lisa Murkowski of Alaska.