WASHINGTON — When it comes to managing Republicans’ best interests, Senator Mitch McConnell of Kentucky, the majority leader, rarely loses. So it is possible that Mr. McConnell views the potential failure of a hastily written health care bill as an eventual boon.

His presentation on Thursday of the Senate’s health care measure to Republican colleagues — after the White House and key lobbyists got a peek the night before — was met with something other than unbridled enthusiasm. According to lawmakers who were at the unveiling, members from the left and right ends of the party’s spectrum were deeply critical of the effort.

As Democrats immediately took to the Senate floor to excoriate the bill and the secretive process in which it was put together, few Republicans, even those involved in crafting it, came to defend it.

A handful of Republicans — more than Mr. McConnell can afford to lose — were quick to disparage the measure. “I have serious concerns about the bill’s impact on the Nevadans who depend on Medicaid,” Senator Dean Heller, his party’s most vulnerable incumbent in the 2018 elections, said of his constituents.