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.