“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, earlier vowed to hold a vote to repeal Obamacare only, but the plan withered within hours after three Republican senators came out against it.
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.

Not a good strategy – Anthony Zurcher, BBC News, Washington

Call it Mr Trump’s “Joker” option for Obamacare repeal. Do nothing, and watch the world burn.
Explaining how your dastardly plan will go down seldom works for cartoon villains, however, and it may not be the best strategy for presidents either.
By telling Americans he’s going to let the US healthcare system collapse in order to rally support for an eventual fix, he’s essentially taking responsibility for anything bad that happens in the coming days. Despite his protestations that he won’t “own” what happens next, he just stuffed the receipt in his pocket.
Premiums go up? Insurance providers pull out of state individual markets? Democrats can say it’s part of the president’s plan to sabotage the system.
All the while Mr Trump’s opponents can point to the Congressional Budget Office’s findings that, without White House meddling, the insurance markets would be relatively stable.
Then again, at this point, the president has few good options. His promises to eventually work with Democrats are undermined by his pledges to defeat them at the ballot box next year. He clearly can’t move forward with Republicans alone.
All that’s left is to walk away and hope for the worst.
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.
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.

The 217-213 vote marked his first legislative victory and goes some way to keeping a key campaign promise to roll back his predecessor’s law.

Democrats say the American Health Care Act will leave millions uninsured.

The bill now heads to the Senate, where Republicans have indicated they will cast it aside and write a new law.

Protesters shouted “Shame on you!” as lawmakers left Capitol Hill after the knife-edge vote.

But there were celebrations moments later on the White House lawn, where the president laid on a reception for Republicans in the House of Representatives.

Six weeks ago, their healthcare attempts appeared doomed when they did not have enough support to have a vote.

But that bill has undergone several revisions to satisfy both the conservative and moderate wings of the Republican party.

“Make no mistake, this is a repeal,” said a triumphant Mr Trump in the Rose Garden. Obamacare, he added, was “essentially dead”.

“Premiums will be coming down, deductibles will be coming down, but very importantly it’s a great plan.”

What do Democrats say?

The Democrats think the effect of this bill would be the opposite, stripping insurance from the poor, giving tax breaks to the wealthy and casting doubt on health provisions for the chronically sick.

“Thousands of Americans would die because they would no longer have access to care,” said Senator Bernie Sanders.

Groups representing hospitals and doctors have also expressed concerns about the Republican plan, which they say has yet to be properly assessed.

The ill-fated Republican bill in March would result in 24 million more Americans losing insurance within a decade, the nonpartisan Congressional Budget Office said at the time.

What changed since March?

One amendment added since then to placate conservatives means states can opt out of providing essential benefits such as cancer treatment and emergency room visits.

And when $8bn (£6.2bn) over five years was thrown in towards coverage for sick people who otherwise might face higher costs, several moderate Republicans changed course and backed it.

About 20 million Americans gained healthcare coverage under President Barack Obama’s 2010 Affordable Care Act, but Republicans viewed it as an overreach of the federal government and said patients had less choice and higher premiums.

The New York attorney general said on Thursday evening that he would challenge the bill in court if it became law, on the basis that it would deny people access to care.

What happens now?

The bill, if it becomes law, would mark a major overhaul in the US health system.

But key elements could be ditched by Republican senators, who have said they will start fresh.

Republican Senator Lisa Murkowski said she would like “a clean slate”, while Senator Bob Corker said the current bill has “zero” chance in the Senate.

The party controls the chamber 52-48, meaning it can lose no more than two Republicans in order for it to pass.

If the Senate passes its own bill, the plan then goes back to the House for approval or more negotiations and amendments.

What does it mean for Trump?

Anthony Zurcher, BBC News, Washington

Round one of the battle over Obamacare repeal is in the books. Round two is set to begin, with the opponents more powerful and the obstacles more imposing.

It’s worth remembering that passage of the Republican healthcare plan in the House of Representatives was supposed to be the easy part. House Speaker Paul Ryan had a sizeable majority at his disposal and the political tools to reward support and punish transgressions.

Instead the American Health Care Act’s long, laborious journey exposed divisions within the Republican Party and the limits in Donald Trump’s powers of persuasion. These challenges won’t disappear. The fault lines will be put under greater pressure and Mr Trump’s skills will be further tested when action heads to the Senate.

Unlike the House, the Republican majority there is narrow, and already some in the party are showing misgivings about the current legislation. Democrats, who have more parliamentary tricks up their sleeves, will attempt to disrupt the process at every turn.

Still, a win is a win. It wasn’t pretty. It may not last. But Mr Trump and the Republican House leadership will take it.

What’s changed from Obamacare?

New bill repeals the individual mandate requiring those who can afford it to have health insurance

Ditches Obamacare requirement for companies with 50 or more staff to provide insurance coverage for employees.

Keeps element allowing under-26s to stay covered on parents’ policies

Enables insurers to charge at least five times as much to older customers.

States can opt out of essential benefits like emergency care and cancer treatment

And they can waive the guarantee to provide healthcare to people with pre-existing conditions.