But Ryan was already facing a backlash from Republicans in the House Freedom Caucus, who very publicly made clear that they didn't like some key parts of the bill, arguing that this isn't much different from the system forged by Democrats and President Obama.
"We think you have to get rid of Obamacare completely," said Rep. Jim Jordan (R-OH), who wants a vote first on a repeal of the Obama health law - and then have the Congress move towards a replacement.
"We are united on repeal, but we are divided on replacement," said Sen. Rand Paul (R-KY), who has tried to rally Tea Party lawmakers to oppose the GOP leadership bill.
If enough allies of Jordan (in the House) and Paul (in the Senate) were to turn their back on the GOP plan, it could conceivably be derailed, in what would be a major setback for the President.
The GOP health plan is "dead on arrival" said Rep. Dave Brat (R-VA), as he joined other Republican rebels in demanding changes, and raising questions about the plan's future.
But it may be a little early to declare the bill dead, as the President himself quickly made overtures to some of the plan's critics.
Also helping Republican leaders for now is something that has plagued lawmakers who have been under the "Tea Party" or "Freedom Caucus" umbrella in recent years - most of them have very little experience with the nuts and bolts of legislating, and most of them aren't on the key committees dealing with health care.
And that will be very evident on Wednesday, as the first votes start on this GOP health care plan.
When you look at the roster of Republicans on the House Energy and Commerce Committee, and the powerful tax-writing Ways and Means Committee, you don't see names like Jordan, Brat and more.
Instead, you see more experienced GOP hands on those panels, most of them less likely to start some kind of palace coup over health care reform - at least, at this point.
"As Republicans, we have a choice," said Rep. Kevin Brady (R-TX), the chairman of the Ways and Means Committee.
"We can act now, or we can keep fiddling around and squander this opportunity," Brady told a news conference.
As for cost estimates, there won't be any ready from the Congressional Budget Office for these first committee votes.
The emerging GOP plan would have approval this week in a pair of House committees, action as soon as next week in the House Budget Committee, and then a press to get a vote in the full House by the end of March.
Congress is set to leave on a two week Easter break beginning on April 7; Senate Republicans would still like to get that House vote done earlier, so Senators can try to act on that same House health reform bill before the Easter Bunny arrives.
"Obviously we want to do it as soon as possible, but we want to do it right," said Sen. Marco Rubio (R-FL).
The top Republican in the Senate indicated Tuesday that time is of the essence.
"I encourage every member to review (the GOP health bill), because I hope to call it up when we receive it from the House," said Senate Majority Leader Mitch McConnell.