Representative Paul Ryan also said that the improved and refined USA health care bill would increase the number of uninsured Americans by 24 million by 2026 as it reduces the deficit by $337 billion.
"The older person - the person in their 50s and 60s - does have additional healthcare costs than, say, a person in their 20s and 30s".
More moderate Republicans also have issues with the bill.
The USA Today reported that US President Donald Trump is getting deeply involved to bridge the gap in the current American Health Care Act to make it easier for him to push the new US health care bill through the House of Congress.
Despite the tweaks Ryan said the bill needs, he added that he feels "very good" about the legislation's progress and where things now stand.
"The reason I feel so good about this is because the president has become a great closer", Ryan told Fox News Sunday host Chris Wallace.
Poorer, older Americans would be especially hard hit with higher premiums and less generous government assistance to buy insurance.
Ryan at one point said that his party faced the "binary choice" of backing the GOP replacement plan that he and his lieutenants crafted or sticking with an Obamacare health insurance system that was fast collapsing of its own weight and driving up premiums for millions of Americans.
A House vote on the plan is scheduled for Thursday.
"I think there's enough conservatives that do not want 'ObamaCare lite, ' " Paul said on ABC's "This Week". "We need to roll up our sleeves and focus on fixing those problems, rather than trying to rush to some arbitrary deadline".
"That may be the case and that's why as it works through this legislative process, we're looking at it and working with our legislative colleagues to make certain that we've got the kind of plan that actually works for people in the real world - something that the previous administration didn't do", Price said responding to Cassidy's concerns.
Meadows, a North Carolina Republican, also said the changes being considered for the Medicaid program would not go far enough, if they left it up to states to decide whether to put in place a work requirement.