The American Hospital Association (AHA) said current provisions for "our most vulnerable" would be thrown into doubt.
President Donald Trump met lawmakers on Wednesday to rally them behind the bill, after a stormy 24 hours.
Moderate Republicans are concerned people will be stripped of cover, while conservatives sense federal overreach.
The bill, called the American Health Care Act, would replace the signature law of President Barack Obama, so-called Obamacare.
It would:
