What could happen?
- It could collapse if certain rules are changed, which the Trump administration can do
- The amount an average plan has to cover of a person's medical cost could be lessened
- Administration could waive fine currently levied on those not buying coverage
- That could result in healthy people not bothering to buy insurance
Plans by the Republican Party in the United States Senate to repeal Obamacare without replacing it with anything else have been thrown into disarray, after three of the party's senators announced they would not back the latest version of the 'repeal only' plan.
So, is Mr Trump correct in his prediction? And if he is, how exactly would that happen?
Ever since it was enacted in 2010, Obamacare — or, more fully, the Patient Protection and Affordable Care Act — has drawn the ire of Republicans.
When the party had a congressional minority, representatives and senators vowed to repeal it when the numbers shifted, and now the opportunity is theirs.
But repeal and replace has been a tough sell, both inside and outside the party, with Republicans split on how to restructure the system.
Because of that, this week the replace part of the plan collapsed, prompting the Republican Senate leadership to change tack with a 'repeal only' option instead.
But that too now looks unlikely to succeed.
Republicans Shelley Moore Capito of West Virginia, Lisa Murkowski of Alaska and Susan Collins of Maine announced that they would not back the repeal, and Rob Portman of Ohio said he had also concerns about the approach.
So, for now, Obamacare will not be repealed, or replaced.
And that is where Mr Trump's claim that it would instead enter a "death spiral" becomes interesting.
So how would Obamacare collapse?
In a nutshell, Obamacare could collapse by changing the rules that sit underneath the law itself, which the Trump administration gets to write and enforce, within limits.
What is Obamacare?
- Affordable Care Act passed by Congress in 2010
- Promised to help tens of millions of uninsured Americans get health coverage
- Under the plan, people can buy cheap insurance on healthcare.gov
- Most coverage costs less than $US100 per month
- Policies vary according to person's income, location, family size and level of coverage desired
- More than 10 million people now have medical cover under the laws
- Number of uninsured adults reduced by 26 per cent
When they were legislated, the Obamacare reforms were an attempt to more heavily regulate America's private-sector-based system of health care and to expand the limited public system, Medicaid, to cover more low-income earners.
Medicaid is funded by the federal and state governments, and the Trump administration probably cannot wind back the funding without the repeal bill clearing Congress. So that part of Obamacare will probably stay.
The vast majority of Americans are not insured by Medicaid, but by private providers — and that is something the Trump administration could do something about.
One problem that has long bedevilled the American model has been insurance companies unwilling to insure people who were already unwell.
But under Obamacare it became much harder for insurers to refuse to cover sick people.
The Trump administration could undermine that by rewriting some of the rules that govern the private insurance market.
How would rewriting the rules make Obamacare fail?
At present, Obamacare regulates how much coverage insurance companies have to provide customers who are buying their plans.
Dylan Scott, a reporter covering health policy in Washington DC for the website Vox.com, said the Trump administration could change those parts of Obamacare without a new law.
"The things that are written into [the Obamacare] law are pretty broadly defined," Scott said.
"Obamacare requires insurance companies to cover a certain percentage of a person's medical costs, but there's some wriggle room.
"At the moment, the average plan should cover 70 per cent of a person's medical costs.
"But the Trump administration could drop that down to, say, 66 per cent and still say it complies with the letter of Obamacare's wording.
"And we know that the Trump administration has said it would seek whatever means they have to try to reduce the regulatory load."
What is the individual mandate?
Another way to hasten Obamacare's demise would be with the 'individual mandate' — the requirement, set out in Obamacare, that people buy health insurance when they can afford it.
The idea was that, by penalising relatively well-off, healthy people via the tax code when they did not purchase insurance, there would be more money in the healthcare system to better provide for the sick.
But the Trump administration could waive the fine currently levied on some of those not buying coverage.
Scott said that would seriously undermine Obamacare.
"If you don't enforce the mandate, then healthier people might just choose not to buy coverage because they're not paying a financial penalty for doing so," he said.
"That means the people who do buy coverage are more likely to be sick, which means their healthcare costs are likely to be higher, which in turn is going to drive up the insurance premiums.
"That leads to what experts in America call a 'death spiral', where it's only the sickest people who feel like they need to buy health insurance."
So, could that all happen?
Maybe, although Scott said he was reluctant to make any firm call given the famous unpredictability of Mr Trump.
For his part, Mr Trump's theory is that if Obamacare did collapse, Democrats would beg congressional Republicans to come up with ways to fix health care.
But some observers — and the Democratic leadership — think it could work the other way around.
Keith Gaddie, a professor of political science at the University of Oklahoma, said the pressure would be on Republicans, not Democrats, to work out a way forward.
"There are electoral consequences a year from now," Professor Gaddie said.
"Obamacare was always meant to be a stop-gap towards something better — it was meant to be something that could be established to broaden coverage and then go back and improve the system later.
"There's a lot of risk in just letting it fail if you're a conservative.
"One alternative is big electoral backlash."
So what happens if lots of Republicans start to worry about their seats in the lead-up to the midterm elections next November?
Democrats claim the party of repeal and replace might end up having to work out how to make Obamacare work better.