WASHINGTON — Senate Republicans steered toward a potential showdown vote on their long-awaited health care bill next week, despite indications that they’ve yet to solidify the 50 GOP votes they’ll need to avert an embarrassing defeat.

Senate majority leader Mitch McConnell, Republican of Kentucky, said he expected to have a draft of the bill ready Thursday. The measure would peel away much of Barack Obama’s health care overhaul and leave government with a more limited role in providing coverage and helping people afford it.

‘‘We have to act, and we are,’’ McConnell said on the Senate floor.

But later, he simply chortled when asked if he was confident the measure would pass, a victory that would elude him if just three of the 52 GOP senators voted no.

McConnell’s ability to assess and line up votes is considered masterful, and he’s eager to pass legislation fulfilling a keystone campaign promise of President Trump and countless GOP congressional candidates. But underscoring the uncertainty he faces, senators from both ends of his party’s spectrum were grumbling about the bill’s expected contents and the clandestine way it’s being crafted.

‘‘It’s apparently being written by a small handful of staffers for members of the Republican leadership,’’ said conservative Senator Mike Lee, a Utah Republican, using a Facebook video for an unusually public swipe at GOP leaders.

Though a member of the 13-senator working group McConnell had tasked with piecing legislation together, Lee said he’s not seen the emerging bill and ‘‘whole-heartedly’’ shares the frustration of constituents unhappy over the secrecy. He said senators should have seen the measure ‘‘weeks ago’’ if the chamber is voting next week, the goal of top Republicans.