"Well it's a fine needle that needs to be thread. There's no doubt about it," Price responded, acknowledging changes made to the bill to win over conservatives could scare off moderate Republicans.
The far-right House Freedom Caucus is still formally opposed to the bill, and made their stance clear in a tweet Friday.
“The House Freedom Caucus still opposes the GOP replacement bill in its current form,” the group tweeted after Trump’s statement Friday.
The House plan has also received criticism from Republican senators, including Sen. Bill Cassidy, R-Louisiana, who is concerned the House plan would make it harder for poorer, older Americans to afford insurance.
"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.
"So if it needs more beefing up, as you say, for folks who are low-income between 50 and 64 years of age, that’s something that we’ve talked about, that’s something that we’ve entertained and that may happen throughout the process," Price said.