President Donald Trump has said the new Republican healthcare policy should be to allow the current law to collapse.
“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.
The party’s Senate leader, Mitch McConnell, immediately vowed to hold a vote to repeal Obamacare only.
During a speech from the Senate floor, Mr McConnell said Republicans would “push forward” with a plan to repeal Obamacare and replace it with a “two-year, stable transition” period to give Congress time to come up with a replacement plan.
“We should not give up,” Mr McConnell said. “Passing this legislation will provide an opportunity for senators of all parties to engage with a fresh start and a new beginning for the American people.”
President Trump backed that plan on Monday night but changed his tune on Tuesday morning by proposing to simply let Obamacare – which has been marred by rising premiums and dwindling insurance provision – die on its own.
“As I have always said, let ObamaCare fail and then come together and do a great healthcare plan. Stay tuned!” he tweeted.
Without a replacement bill, analysts have estimated that millions of people would lose health insurance.
Three Republican senators, Susan Collins, Shelley Moore Capito and Lisa Murkowski, have said they will not support their party’s plan to repeal Obamacare without a replacement plan.
That meant the repeal-only plan effectively withered within hours.
Republicans believe that Obamacare, which extended insurance to 20 million more Americans, will collapse on its own.
They viewed it as an overreach of the federal government and argue patients have less choice and higher premiums.
The party’s proposed alternative had kept key Obamacare taxes on the wealthy, while imposing sharp cuts to healthcare for the poor and allowing insurers to offer less coverage.
But two Republican senators, Mike Lee and Jerry Moran, said the new legislation did not go far enough in repealing Obamacare.
They joined Senators Rand Paul and Susan Collins, who had already opposed the bill.
Republicans, who hold 52 seats, no longer have enough votes to approve the measure in the 100-member Senate.
Moderate Republicans had also said the bill would have harmed some of their vulnerable constituents.
The non-partisan Congressional Budgetary Office (CBO) found the bill would have stripped 22 million Americans of health insurance over the next decade.
On top of that, polls had shown Obamacare remained popular among Americans – a survey by the Washington Post and ABC News on Monday found more than twice as many people preferred Mr Obama’s programme to the proposed alternative.