And in the economic report of the president, the White House boasted last week about how Mr. Trump had allowed small businesses and individual consumers to buy insurance plans that skirt many requirements of the Affordable Care Act, offering lower costs but fewer benefits.

Under a rule issued in August, Mr. Trump greatly expanded the market for sales of short-term insurance plans that do not have to cover prescription drugs, maternity care, drug abuse treatment or pre-existing conditions.

The House Democrats’ bill would turn back the president’s action by stipulating that short-term plans are included in the definition of “individual health insurance coverage” under the Affordable Care Act and therefore must comply with coverage requirements of the health law.

“These junk plans discriminate against people with pre-existing conditions,” said Representative Frank Pallone Jr., Democrat of New Jersey and an architect of the new legislation. “They deny access to basic benefits. They set arbitrary dollar limits for health care services, leading to huge surprise bills for consumers.”

“We passed the Affordable Care Act to rein in exactly these types of abuses,” said Mr. Pallone, who is investigating the short-term plan as chairman of the Energy and Commerce Committee.

The Affordable Care Act provides two main types of financial assistance to people of modest means buying private insurance: tax credits to help them pay premiums, and cost-sharing reductions to lower their deductibles, co-payments and other out-of-pocket costs.

The House Democrats’ bill would revise the law to provide more of both types of assistance.

In addition, the bill would make subsidies available to some working families who are now ineligible. The law, as interpreted by the Internal Revenue Service, bars subsidies to workers who have access to affordable employer-sponsored coverage for themselves — even if the cost of coverage for the entire family is unaffordable. The House Democrats’ bill would eliminate this quirk in the law, sometimes called the family glitch.