Adding pressure to fix the administration’s problem-plagued health care program, former President Bill Clinton said Tuesday that President Barack Obama should find a way to let people keep their health coverage, even if it means changing the law.

Clinton said Obama should “honor the commitment that the federal government made to those people and let them keep what they got.”

The former president, a Democrat who has helped Obama promote the 3-year-old health law, becomes the latest in Obama’s party to urge the president to live up to a promise he made repeatedly, declaring that if Americans liked their health care coverage, they would be able to keep it under the new law.

Instead, millions of Americans have started receiving insurance cancellation letters. That, coupled with the troubled launch of the health care law’s enrollment website, has prompted Republican critics and frustrated Democrats to seek corrections in the law.

House Republicans have drafted legislation to give consumers the opportunity to keep their coverage. Ten Senate Democrats are pushing for an unspecified extension of the sign-up period and in a private White House meeting last week several pressed Obama to do so. Sen. Mary Landrieu, D-La., has proposed legislation that would require insurance companies to reinstate the canceled policies.

White House spokesman Jay Carney on Tuesday reiterated the White House argument that the cancellations apply to only about 5 percent of Americans who obtained health care insurance. He also argued that more than half of those people receiving termination notices would benefit from better insurance at lower prices either through expanded Medicaid or through new health care marketplaces.

For the remainder, Carney said, “The president has instructed his team to look at a range of options.”

The issue facing the administration now is how to ease the impact on people who are losing their plans and don’t qualify for subsidies to cover higher premiums. Carney said the White House opposes a House Republican bill, proposed by Rep. Fred Upton, R-Mich., that would allow insurers to keep selling insurance that doesn’t offer the type of benefits required by the new law.

“Any fix that would essentially open up for insurers the ability to sell new plans that do not meet standards would create more problems than it fixed,” he said.

Jonathan Gruber, a Massachusetts Institute of Technology economist who advised the Obama administration on the health care law, said the White House has few if any administrative options available.

One solution, he said, would be to offer a “transitional tax credit” to those consumers who are losing their insurance and must pay more for new coverage that meets the law’s standards.

“I don’t know how you do that without Congress’s permission, and they’re not going to give it to you,” he said.