President Trump boasted last week that millions of people are joining association health plans, one alternative to Obamacare that he's planning to expand.

"Now here's the good news. We've created associations, millions of people are joining associations. Millions. That were formerly in Obamacare or didn't have insurance. Or didn't have health care. Millions of people," he said in an interview with the New York Times. "It could be as high as 50%. You watch. So that's a big thing."

Association health plans, along with short-term health policies, are at the heart of Trump's drive to increase choice and lower costs in the health insurance market -- and chip away at the Affordable Care Act.

However, no one has joined these new associations yet. The Trump administration has yet to act on the president's executive order that would expand access to these groups.

Trump unveiled the executive order in mid-October, shortly after Congress ran out of time to repeal and replace Obamacare. Federal agencies still haven't released proposed regulations, though Trump's directive gave them 60 days to consider doing so.

The Department of Health and Human Services declined to comment. The Department of Labor and Office of Management and Budget did not return requests for comment. Health policy experts expect the proposed rules to be issued this month. Then, it could take weeks or months for the insurance plans to appear on the market.

Related: Trump begins Obamacare dismantling with executive order

The president says the executive order will boost competition, give consumers more options and lower premiums. Critics, however, argue that these policies would provide skimpier coverage and would raise the cost of plans on the Obamacare exchanges by siphoning off younger and healthier consumers.

Much will depend on how the new regulations are written, but here are the kind of policies Americans could buy if Trump's plan is realized:

Association health plans: These plans are usually sponsored by trade organizations or interest groups. Small businesses, and possibly individuals, could find it easier to obtain health insurance through association health plans, which would let them leverage their greater numbers to secure less expensive policies.

Association health plans have existed for decades, though they have a long history of fraud and insolvency, which left some policyholders and providers on the hook for millions of dollars in unpaid claims, said experts from Georgetown University's Health Policy Institute. The Affordable Care Act largely eliminated their advantage because it required the plans to meet the same comprehensive regulations as the small business insurance market.

The Trump administration could amend the rules governing these plans so they are no longer subject to state regulation, said health policy experts. Instead, the nationwide plans may come under the same federal oversight as large-employer policies, which are not subject to all of Obamacare's mandates. For instance, large-employer plans don't have to provide comprehensive coverage that includes prescription drug, substance abuse and maternity benefits. Eliminating these would make plans less expensive, but could leave policyholders who need these benefits out in the cold.

Have you belonged to an association health plan or do you wish to join one? Is a short-term health insurance policy right for you? Email healthcarestories@cnn.com and you could be included in an upcoming article.

Also, small businesses with sicker workers could find themselves paying higher premiums than their peers with a healthier workforce. While companies can't exclude or charge higher premiums to individual workers based on their pre-existing conditions, the rates an employer pays as a whole are based on the health status of its workers. Under Obamacare, a small business' premium is not determined by its workers' medical history.

Related: How Trump's executive order can hurt those with pre-existing conditions

Association plans also could try to cherry pick small businesses with younger and healthier staffers by charging very high premiums or offering skimpier benefits to firms with older and sicker workers or those with more women, who tend to use more health care services.

Short-term health plans: The Obama administration limited the duration of short-term health plans to no more than 90 days in order to make them less attractive. The executive order is expected to lift that cap, enabling consumers to buy policies that would last just under a year.

The advantage: Short-term plans don't have to adhere to Obamacare's regulations so consumers would have a wider array of options with lower monthly rates.

The disadvantage: These policies can exclude those with pre-existing conditions or base rates on consumers' medical history. They can also offer skimpier benefits so policyholders may have to pay more out of pocket if they actually need care.

"If someone is healthy, they could have the option of a less expensive, less comprehensive policy, but there is a risk," said Cori Uccello, senior health fellow at the American Academy of Actuaries.

Related: What's in Trump's health care executive order?

These plans have also been around for a long time, but those who have them are not considered insured and are subject to the Obamacare penalty. Of course, that won't be a concern starting next year since Congress has effectively repealed the individual mandate requiring nearly all Americans to have coverage.

States would likely retain oversight of these policies and could impose their own rules, said Sabrina Corlette, research professor at Georgetown's Health Policy Institute. For instance, New York and New Jersey currently don't let insurers sell short-term plans that don't comply with Obamacare -- and no short-term plans are available in either of those states.

At least two major insurers have indicated they are eager to expand their offerings.

UnitedHealth (UNH) already has about 300,000 members in association health plans. The performance is strong and "generally in keeping with our broader portfolio," Dan Schumacher, the insurer's president, said in its October earnings call. UnitedHealth is also "excited" to see the duration of short-term policies extended, he said.

At Aetna (AET), CEO Mark Bertolini said the company is looking to jump start its short-term policy offerings.

"We are actually looking at reenergizing a program we had prior to the ACA, but [with] more [of] a focus [on a] short-term, one-year kind of plan, or transition plan, versus just the skinny benefit, which leaves a lot of people at some moral harm at some point," he said in the company's October earnings call. "And so we have to think about what kind of plan it would look like ... we're already all over that. As soon as the executive order came out, we were on top of it."

The executive order would also expand employers' ability to give workers cash to buy coverage elsewhere under a system known as health reimbursement arrangements. The agencies were given 120 days to propose these regulations.