Trump also specifically tweeted about the possibility of ending subsidy payments the federal government makes to insurance companies, which reduce premiums and out of pocket costs for lower-income Americans who buy their own insurance on the individual markets.
On July 29, Trump said in another tweet, "If a new HealthCare Bill is not approved quickly, BAILOUTS for Insurance Companies and BAILOUTS for Members of Congress will end very soon!"
Under current law, these federal payments, also known as cost-sharing reductions, or CSRs, are made directly to insurance companies to keep prices down.
The Kaiser Family Foundation estimated that if these CSR payments were stopped, insurance premiums on the individual markets would increase by 19 percent or higher.
Experts fear many Americans who have relied on subsidized insurance will no longer be able to afford individual plans and insurance companies may simply choose to withdraw their plans from marketplaces altogether, only selling privately or to groups.
Insurance companies may also read an end to subsidies as a signal about government intentions.
"Some insurers may also interpret a decision to stop these reimbursements as evidence that the Administration wants the market to fail, causing them to exit the market entirely," Matt Fielder, a fellow at the USC-Brookings Schaeffer Initiative on Healthy Policy, explained to ABC News.
"Those types of exits could leave some consumers with fewer options or, in some cases, no options at all," he added.
An upcoming monthly payment of federal subsidies is set for the third week of August. Lawmakers on both sides of the aisle have expressed concerns that abruptly ending payments could dramatically disrupt the health care system and send the individual markets into a tailspin.
White House press secretary Sarah Sanders said at a press briefing last Wednesday that no final decision has been made regarding what the administration plans to do about CSR payments.
The president and his Cabinet have other options that could immediately affect the system, according to health care and legal experts.
In addition to ending the CSR payments, the government could stop enforcing the individual insurance mandate, which requires Americans to purchase health insurance or pay a tax.
In theory, should Trump order his secretaries to no longer enforce that part of the law, some healthier, younger Americans may choose to forgo coverage. This could leave insurers with imbalanced markets, tilting toward sicker, older populations.
The threat alone of ending the individual mandate has led some companies to consider an increase in their prices. In a June 1 press release, Pennsylvania insurance commissioner Teresa Miller warned that if the individual mandate is ended, companies estimate a 23.3 percent rate increase statewide. As a Blue Cross Blue Shield Association statement read last Wednesday, “A system that allows people to purchase coverage only when they need it drives up costs for everyone."
The president could also try to shuffle around the current set enrollment periods when an individual can sign up for a health insurance plan. Executive efforts to decrease enrollment period sign-ups have already been in the works. The administration proposed shortening the enrollment period for 2018 from three months to about six weeks, thereby cutting the amount of time people have to sign up for insurance plans, further destabilizing the insurance markets.
The marketplace is also supposed to pay navigators to offer “free, objective, and trained help” on choosing insurance plans and clarifying questions about the enrollment process, as Karen Pollitz, a senior fellow at The Kaiser Family Foundation, explained to ABC News. However, Politz said that the House Appropriations Committee recently released a draft of a bill that would cut the U.S. Health and Human Services Department spending on navigators.
In January, the president cut funding for advertising that was aimed at young adults to sign up for plans by the end of open enrollment. For the first time, there was a dip in sign-ups at the end of open enrollment period, Pollitz said, where usually companies see a surge.
ABC News' MaryAlice Parks contributed to this report.