Story highlights Most members haven't seen legislative texts of Republican senators' health care bill

Across Capitol Hill, House conservatives are also growing a bit nervous with the lack of clarity

Washington (CNN) Senate Majority Leader Mitch McConnell might be on the verge of releasing a bill to repeal Obamacare, but he's got conservatives to convince before he can be sure he has the votes to pass it.

On Tuesday, McConnell announced there would be a "discussion draft" unveiled Thursday on health care, but some in the right flank of his conference are already voicing skepticism for what's coming.

"I think they've forgotten all the rallies where we said we're going to repeal it. We had thousands of people standing up and cheering us on, saying we're going to repeal it and now they've gotten pretty weak-kneed and I think they want to keep it," Sen. Rand Paul, a Kentucky Republican, told reporters Tuesday. "Conservatives who are in the know are going to know that this isn't repeal."

Most members haven't seen legislative texts of the bill, but the process itself has been deeply frustrating for some of the conservatives who McConnell may need to convince to pass his bill.

Tuesday afternoon Republican Sen. Mike Lee of Utah took to Facebook Live to tell constituents, "if you're frustrated by the lack of transparency in this process, I share your frustration. I share it wholeheartedly."

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