The Trump administration and House GOP leaders are making two significant changes to the ObamaCare replacement bill ahead of an expected vote on Thursday.
Ryan said on "Fox News Sunday" that he feels "very good" about the bill's prospects.
Meanwhile, a key conservative senator said White House officials were continuing to negotiate through the weekend on even more dramatic revisions to the bill in hopes of winning over hard-liners who have threatened to tank the legislation.
Ryan said the more generous tax credits will be among the changes the House Rules committee will take up this week in advance of a final House floor vote - planned for Thursday.
"We have to do something about the fact that the House bill disproportionately affects older, rural Americans", Republican Senator Susan Collins of ME said on NBC's "Meet the Press" on Sunday.
"There's no doubt about it", Price responded, acknowledging changes made to the bill to win over conservatives could scare off moderate Republicans.
Senator Tom Cotton, a conservative Arkansas Republican, said that the bill would not reduce premiums for people on the private insurance market. As the bill now stands, older, poorer Americans will have far less help from Republican tax credits starting in 2020 than they get through Obamacare subsidies.
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"Just yesterday President Trump made it clear - he supports the bill 100 percent, and we all do", he said.
But Sen. Rand Paul (R-Ky.), who has worked closely with the hard-right bloc in the House, said on "This Week" that the bill was still short of a majority.
"If Republicans hold a big press conference and pat ourselves on the back that we've repealed Obamacare and everyone's premiums keep going up, people will be ready to tar and feather us on the streets and quite rightly", Cruz said.
Cruz said he can't vote for a bill that allows health insurance premiums to continue to rise.
Dear Editor: Since resistance has grown and it will certainly be amended, it is not necessary to debate too many details of the Trump-Ryan health care plan that Paul Ryan presented recently.
Speaking on NBC's Meet the Press, Republican Senator Susan Collins of ME said she was concerned about a report from the Congressional Budget Office that said 14 million people would lose health coverage under the House bill over the next year and 24 million over the next decade.
"We're still having conversations with our members".