WASHINGTON — Facing a rebellion within their own ranks, Senate Republican leaders on Tuesday postponed a vote to overhaul the 2010 Affordable Care Act until after the July Fourth recess. The current proposal by Senate Majority Leader Mitch McConnell, R-Ky., would cause an estimated 22 million more Americans to be uninsured by the end of the coming decade while reducing federal spending by $321 billion during that time, the Congressional Budget Office concluded Monday. The forecast by Congress’ nonpartisan budget scorekeepers appeared to rapidly erode Republicans’ confidence in the bill, with at least five GOP lawmakers saying that they would vote against even a procedural motion to start debate. In a sign of the challenge Senate Republicans face in mustering enough votes, Majority Whip John Cornyn, R-Texas, said the procedural vote is likely to be scheduled for Wednesday rather than Tuesday. Members who have publicly come out in opposition are facing a full-court lobbying press from party leaders.