The Kaiser Family Foundation said Thursday that 4.5 million people could obtain insurance at essentially no cost next year because they are eligible for financial assistance that could pay the entire cost of a bronze plan, the minimum level of coverage that meets federal requirements.

Insurers have raised the premiums for many health plans in 2018 because of Mr. Trump’s threat to cut off certain subsidies paid to insurers — a threat he carried out last month. Many consumers with low or moderate incomes are eligible for larger tax credits to help pay the premiums. As a result, many consumers can buy similar health plans or more generous plans for about the same price as last year.

Republican attacks on the Affordable Care Act appear to be fortifying support for the law.

The new report from the Trump administration came two days after voters in Maine approved a ballot measure to expand Medicaid under the health law and a Democrat swept to victory in Virginia in a governor’s election in which health care was a top issue.

The sign-up period for the federal exchange ends Dec. 15 and is about half as long as the open enrollment season in each of the past three years.

The number of new customers signing up for insurance is a closely watched indicator of public interest in the marketplace. The number of new customers selecting health plans on HealthCare.gov averaged 34,300 a day last week, up from 26,400 in the first week of open enrollment in 2015 and 20,500 last fall.

The new report shows sign-ups by people in 39 states that use HealthCare.gov. It does not include activity in 11 states that operate their own insurance exchanges. Some people who sign up do not pay their share of premiums for the first month, so the coverage never takes effect. Others allow coverage to lapse during the year because they obtain insurance from another source or fail to pay premiums.

Health policy experts said that unhealthy people with the greatest need for insurance tended to sign up in the first weeks of the open enrollment period while healthy people, who are needed to stabilize the market, were more likely to sign up near the final deadline. It is, they said, too early to predict total enrollment for 2018.