Sen. John Cornyn John CornynCalls grow for Biden to expand election map in final sprint Bipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection MORE (R-Texas) is measuring support for a new bill to repeal and replace ObamaCare as lawmakers head toward an end-of-the-month deadline.

"What I told Senator Graham is we would work to try to get a sense of where people were ... so my hope is we'll get that preliminary information back in the next few days," Cornyn said, when asked about the vote counting.

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He added the process could also identify members who are undecided or have follow up questions.

Instead, the bill would convert the funding into block grants to states.

But the legislation faces an uphill effort to getting through the Senate by the end of the month—when the special budget rules that allow the healthcare bill to pass by a simple majority will expire.

Republicans are currently waiting to get a score back from the Congressional Budget Office (CBO), which would say how much the bill would cost and how many individuals would gain or lose insurance coverage.

They would also need to win over at least 50 Republican senators, which could be an uphill battle after they failed to clear a "skinny" ObamaCare repeal bill in July and with many of their colleagues eager to move on.

The bill was also discussed during the closed-door GOP caucus lunch on Thursday, with Graham and Cassidy making a presentation.

"He encouraged everybody to jump on board....I'm very pleased with the leader's response," Graham said. "He encouraged everybody to jump on board....I'm very pleased with the leader's response," Graham said.

The GOP senator added that "I can tell you this if we had a vote right now we would get 47, 48 votes."

The vote-counting process, known as "whipping," will give GOP leadership a tentative count of which senators support the legislation spearheaded by GOP Sens.(S.C.) and(La.).