"This is our chance to bring about changes we've been talking about since Obama Care was forced on the American people," McConnell added.
"If you support the larger effort to repeal and replace Obama Care, you should at the very least want to have a debate on this bill," said Sen. Orrin Hatch (R-UT).
But there was no guarantee that the debate would begin next week on the Senate floor, as a handful of GOP Senators withheld their support.
"It is very likely that I will vote no on the motion to proceed," said Sen. Susan Collins (R-ME), though she left herself some wiggle room in relation to how the plan is scored by the Congressional Budget Office.
With Sen. Rand Paul (R-KY) also expected to vote "No," GOP leaders were quickly at the point where they cannot lose any more votes on the health care bill.
As for the details of the new Senate health care bill, the biggest change was the addition of a plan from Sen. Ted Cruz (R-TX) and Sen. Mike Lee (R-UT), which would allow insurance companies to sell lower-cost, lower-coverage insurance plans, as long as they sell regular policies that follow the requirements of the Obama health law.
"This is a critical step in the right direction and I will continue to work closely with my colleagues to unite our conference around a bill that can pass," Cruz said in a statement.
"The inclusion of this language is a step in the right direction," said a statement by the conservative group Freedom Works, which has tried to pressure the Senate to act on a bill to make major changes in the Obama health law.
But other changes also disappointed some on the right, as the revised bill will keep several taxes in the original Obama health law - one that levies a 0.9% Medicare payroll tax on more wealthy Americans, and a 3.8% tax on investment income.
Both would apply to those making over $200,000 per year as an individual, or $250,000 for couples who file joint returns.
The new GOP bill would also maintain a provision that allows insurance companies to write off high value compensation to company executives.
The GOP health bill that was approved by the House in early May targeted all three of those tax plans for repeal.
But the new provisions won't matter if the bill can't muster 50 votes.
Capito and several other Senators met privately with the Senate Majority Leader a few hours after the revised bill was unveiled - it wasn't clear whether more changes to the GOP plan were coming.
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