The widespread dissatisfaction among House and Senate lawmakers - conservatives and moderates alike - showed no signs of dissipating early in the week, posing a serious challenge for Ryan as he searches for enough votes to pass the legislation on the House floor.
Ryan urged senators to amend the measure once it reaches the Senate - an outcome that remains in doubt as more and more House Republicans express concerns.
"It's a very good start. It's actually an excellent start," Ryan said of the bill, known as the American Health Care Act.
"The point is, we had a plan. We have a plan. We're moving this plan. And we're making fine-tuning refinements to this plan as it goes through the legislative process," he said.
On Tuesday, the White House began its own effort to salvage support for the plan, even as conservatives with Trump's ear told him the bill could be a political trap.
In a separate interview Wednesday, Ryan countered reports that White House support for the bill might be softening under criticism from Trump's allies. He had spoken to Chief of Staff Reince Priebus and chief strategist Stephen K. Bannon about it "a number of times" and noted that Trump has brought lawmakers to the White House to make the case for the legislation.
"We are on the same page as the White House," Ryan told conservative radio host Laura Ingraham. "I think there are those who would love to wedge us for one reason or another, but that's just not the case."
On Tuesday, one day after the Congressional Budget Office (CBO) released its analysis showing that 14 million fewer Americans would be insured next year under the GOP plan, Vice President Mike Pence and Health and Human Services Secretary Tom Price went to Capitol Hill to tout the proposal.
Still, key lawmakers continued to voice opposition.
"I have serious concerns about the current draft of the House bill," Sen. Ted Cruz (R-Tex.) said in an interview. "As written, I do not believe the House bill would pass the Senate."
Cruz went to the White House on Tuesday along with a small group of fellow conservatives to discuss health care.
The legislation will face an important test Thursday, when the House Budget Committee meets to combine pieces passed by separate panels into a single bill and advance it to the House floor. The budget panel cannot make substantive changes to the legislation, but it can make nonbinding recommendations before it reaches a final vote.
House Budget Committee Chairman Diane Black (R-Tenn.) insisted that GOP leaders are not "dug in" when it comes to concerns about the measure.
"Oh, no, no," she said Wednesday when asked by conservative radio host Hugh Hewitt. "We're listening. We're definitely listening. And I will tell you: Tune in to our Budget Committee tomorrow, and you will hear these conversations. You may hear some actions that are taken about sending a message on to the Rules Committee."
Several members of the hard-line conservative House Freedom Caucus sit on the Budget Committee and could decline to support the bill, which they have argued would not go far enough in pulling back elements of the Affordable Care Act (ACA). Republicans hold an eight-vote advantage over Democrats on that committee, and if four GOP members oppose the bill, they can stall its progress. Three of the panel's 22 Republicans are members of the House Freedom Caucus.
Aides to those three members - Reps. Dave Brat (Va.), Gary Palmer (Ala.) and Mark Sanford (S.C.) - did not respond to inquiries Tuesday about whether they intended to support the legislation in committee, while three other Budget Committee Republicans - Reps. John Faso (N.Y.), Mario Diaz-Balart (Fla.) and Bruce Westerman (Ark.) - said they were undecided.
Ryan told Ingraham on Wednesday that the legislation had been subject to "a lot of misinformation and confusion" and said leaders "want members to improve these bills."
He lauded the proposed changes to Medicaid, cutting expenditures by nearly $900 billion over 10 years: "It's the biggest entitlement reform we've ever had. This is bigger than welfare reform."
On Tuesday night, he told Fox News Channel that "of course" leaders are open to changes.
"Yes, we are, but we've got to make sure we hit the sweet spot - so keep consensus, and we've got to get it done," he said. "We don't want to have some endless, dragged-out thing where we never get this done."
Senate Majority Leader Mitch McConnell (R-Ky.) attempted to play down the severity of the GOP split Tuesday after a closed-door party lunch attended by Pence, Price and some of the architects of the House bill, including Ways and Means Committee Chairman Kevin Brady (R-Tex.).
Speaking with reporters, McConnell tried to shift the focus from the coverage numbers to more favorable terrain for Republicans: the CBO's projection that Ryan's plan would reduce the federal deficit over the next decade and produce a 10 percent average decrease in premiums after that.
"We are hoping to have a more vibrant market that will attract a greater number of people to actually be able to buy, at an affordable cost, insurance that actually makes sense for them rather than one prescribed by the government," McConnell said.
Sen. Bob Corker (R-Tenn.) was more guarded than usual with reporters as he left the meeting. He declined to discuss specifics but said House leaders and the White House were making a good-faith effort to hear the concerns of Republican senators.
"They really are taking input. So I don't think they would be over here unless they really do want to take input from folks," he said.
Meanwhile, Rep. Mark Meadows (R-N.C.), the head of the Freedom Caucus, said Tuesday that there's "some work to do, still" on the measure. He added that he had received "no assurances" from the White House or Republican leaders about changes that would attract his support.
The House Republicans' legislation would keep a few of the ACA's most popular features, such as forbidding insurers from denying coverage or charging more to people with preexisting medical problems, and allowing young adults to stay on their parents' insurance policies until age 26.
The plan would erase penalties the ACA imposes on people who do not buy health coverage and, instead, would have a deterrent: a 30 percent surcharge on premiums that insurers could levy for a year if consumers let their coverage lapse. The bill would remove the ACA's subsidies, replacing them with new tax credits and insurance rules that, together, would provide more help to younger people than older ones. The tax credits could be used for any plan sold in a state as long as it didn't provide coverage for abortion.
The legislation would gradually eliminate an expansion of Medicaid, the public insurance program for lower-income Americans, that was accepted by 31 states under the ACA and would give states an annual fixed sum based on the number of people in the program.
Moderate Republicans from states that expanded Medicaid have voiced concerns that the bill would not do enough to protect those who obtained coverage through that expansion.
Rep. Charlie Dent (Pa.) - a leader of the moderate GOP faction in the House - said he has "serious concerns and reservations" about supporting the measure without changes.
Reps. Ileana Ros-Lehtinen (R-Fla.) and Leonard Lance (R-N.J.), two other moderates, said Tuesday that they would oppose the bill.
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What's next for the Affordable Care Act replacement bill
Republicans' first legislative priority is to "repeal and replace" the Affordable Care Act, more commonly known as Obamacare. Below is a guide to the three-phase process they plan to take.
By Kevin Schaul and Kevin Uhrmacher
Latest action: March 13
Bill scored by Congress's budget analysts
A Congressional Budget Office analysis of the bill estimated that 14 million additional people would be uninsured next year if AHCA were enacted. That number jumps to 24 million by 2026, partially because federal Medicaid dollars per person would be capped, imperiling the expansion of the program that took place in 31 states and the District of Columbia. The report also estimated a $337 billion reduction in the federal budget over 10 years.
The CBO is a nonpartisan scorekeeper that predicts the impact of legislation. Two House committees voted the legislation through before the CBO released its analysis, prompting criticism from Democrats.
Before it was released, some Republicans tried to preemptively downplay or discredit the report, with others calling on their House colleagues to pump the brakes and wait for the budget estimate before proceeding.
Expected this week
Bill moves to Budget Committee
Here, the two individual bills will be combined into one piece of legislation that will eventually go on to a full vote on the House floor. The Budget Committee chair, Rep. Diane Black (R-Tenn.), will serve an important procedural role in the process.
Bill goes to the Rules Committee
The Rules Committee will consider amendments from the budget chair, Black, who works with leadership to find solutions that can help get the necessary votes for passage.
Planned for week of March 20
Bill must pass House
House Speaker Paul D. Ryan (R-Wis.) has said he hopes to schedule the full floor vote for the week of March 20. Amid a chorus of complaints from the House Freedom Caucus and conservative think tanks, as well as moderate Republicans concerned about how many Americans could lose insurance coverage, it is unclear whether House leaders have enough votes.
Bill must pass Senate
Because Republicans hope to pass this legislation under the less-onerous budget reconciliation process, House leaders must take care that the bill they pass will comply with the "Byrd Rule" in the Senate. Generally, the rule says a reconciliation bill must relate to the budget, which means some of the Affordable Care Act's provisions cannot be addressed via this process because they do not deal with taxes or spending. It also stipulates that the law cannot add to the deficit in the long term (10 years after it is implemented). It will be up to the Senate parliamentarian to decide whether the legislation meets the Byrd Rule standards.
The upside of doing it this way: Reconciliation bills are fast-tracked through the Senate and will need only 50 votes to be brought to a vote.
It's also possible that the Senate will do a significant rewrite of the legislation, moderating it but also setting up a showdown with House Republicans aiming for a more conservative approach.
If the House and Senate bills are not identical, a conference committee is formed
A group of lawmakers from the two chambers irons out the differences between the bills, which are then presented to both chambers for a final up-or-down vote.
President signs the bill into law
If Trump sours on the bill, he could decide to veto - effectively killing the legislation. Or he could sign it, kicking off the next phases of the Republican effort to dismantle the Affordable Care Act: further regulatory actions and additional legislation.
Last year, an Affordable Care Act repeal bill cleared both houses but was promptly vetoed by President Barack Obama in defense of his signature policy accomplishment.
Beyond the AHCA, Republicans have outlined two other phases of health-care overhaul. The first of those is an easing of regulations, begun by Trump's Jan. 20 executive order telling federal agencies to "minimize the unwarranted economic and regulatory burdens" of the Affordable Care Act. Regulatory reforms could include narrowing the list of benefits that the Affordable Care Act requires insurers to cover.
Because only budget-related items are allowed in a reconciliation bill, Republicans also plan to address other aspects of the replacement with at least one other piece of legislation. This bill would be subject to the filibuster, requiring 60 votes - and at least eight Democrats - to get to a Senate floor vote. It could include allowing people to buy insurance across state lines.
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Source: Staff reports, Committee for a Responsible Federal Budget, Congressional Budget Office [PDF]. Published March 13.