“I’m not going to own it,” Mr Trump told reporters of Obamacare, “I can tell you the Republicans are not going to own it.”
Support for the Republican Senate bill fell apart on Monday when two more senators said they could not back it.
Senate Democratic leader Chuck Schumer said Mr Trump was “playing a dangerous game” with the US healthcare system.
“He is actively, actively trying to undermine the healthcare system in this country using millions of Americans as political pawns in a cynical game”, Mr Schumer said on Tuesday.
Republican Senate leader Mitch McConnell vowed to hold a vote to repeal Obamacare only, but the plan withered within hours after three Republican senators came out against it.