WASHINGTON — Republicans want to replace the Affordable Care Act with “universal access” to health care, House GOP members said.

The goal is to ensure that everyone can buy or find coverage, a House leadership aide said at a briefing organized by top Republicans.

The briefing came amid growing concern about the 20 million people who have gained health insurance under the ACA, reducing the percentage of uninsured Americans to below 10%. The American Medical Association said that “any new reform proposal should not cause individuals currently covered to become uninsured.”

Rep. Kevin Brady, (R., Texas), chairman of the Ways and Means Committee, said “scare tactics” were enveloping the issue, and promised that Obama­care plans would not be terminated with President-elect Donald Trump’s inauguration.

To say that 20 million people will lose insurance is a “big lie,” Brady said. “Republicans will provide an adequate transition period and give people peace of mind.”

The leadership aide said that while overturning major elements of the ACA was a priority for the first 100 days of the Trump administration, the move to a replacement plan could take up to three or four years.

The federal online insurance exchange, meanwhile, saw its busiest enrollment day ever, when 670,000 people signed up for an Obamacare plan on December 15. Citing a late rush, the Obama administration extended the deadline to sign up for 2017 plans by four days.

As of the start of winter, a record 6.4 million people had enrolled for plans, 400,000 more than at the same point in 2015. The numbers “confirm that some of the doomsday predictions about the marketplace are not bearing out,” said Department of Health and Human Services secretary Sylvia ­Burwell.

Also last month, the Centers for Medicare & Medicaid Services (CMS) finalized changes affecting online exchanges’ permanent risk-adjustment program, which moves money from insurers with lower-cost enrollees to plans with higher-cost members. Risk adjustment in 2018 will now take into account the effects of people who are enrolled for only part of the year, and prescription drug data will be included in its formula. Policy makers regard the changes as crucial to stopping insurers from abandoning the ­exchanges.

“The administration will leave the marketplace on a stable path that, when fully implemented, will ensure quality coverage is available for all Americans well into the future,” said CMS acting administrator Andy Slavitt.

Concern about elimination of the ACA also prompted insurance companies to step up their lobbying to avoid changes that they say could throw the exchanges into disarray. Ending subsidies for the individual mandate is especially worrisome, they say, as they plan 2018 coverage around risk ­projections.

And the Council of Economic Advisers issued a report saying the big increases in Obamacare 2017 premiums “are a one-time pricing correction, not a harbinger of future market instability.” Next year’s hikes do not undermine the overall stability of the individual health plan market, it added.

The report also said the average premium for people who have employer-based health insurance — most Americans — was $3,600 lower than it would have been if premiums had risen at the rate they were climbing in the decade before the ACA was enacted.

The ACA “has really meant something to everyone, not just the people who didn’t have insurance,” said council chairman Jason Furman. “People who had insurance get a range of protections like free prevention, coverage from preexisting conditions, and no lifetime and annual limits.”

And HHS released an extensive compilation of national and state-level data illustrating the substantial improvements in health care for all Americans under the ACA. Beyond people who would otherwise be uninsured, millions of Americans with employer, Medicaid, Medicare, or individual market coverage have benefited from new protections as a result of the law, the department said.

“As our nation debates changes to the health care system, it’s important to take stock of the historic progress in recent years,” said Burwell. “Whether they get their coverage through an employer, Medicaid, the individual market, or Medicare, Americans have better health coverage and health care today as a result of the ACA. Millions of Americans with all types of coverage have a stake in the future of health reform, and it’s time to build on the progress we’ve made, not move our system backward.”