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“The industry is saying 10-15-20 percent,” the spokeswoman said in an email. “Once our members pay their binder they are pretty good at paying.”

Mr. Obama’s claims about the ages of enrollees was also only for those in the 36 states that are using the federal exchange marketplace. It’s unclear whether that number holds up in states that set up their own exchanges.

Just like the federal government, which gave enrollees extra time to apply if they said they at least started their applications by the March 31 deadline, many states did the same.

California, one of those states, announced Thursday that it signed up an additional 200,000 people in the extra enrollment time allowed this month.

Outside of the exchanges, 3 million young adults have been able to stay on their parents’ plans because of the law, and an additional 3 million people had signed up for Medicaid coverage through the end of February, the White House said. Enrollment in Medicaid, a government-funded health care program for the poor, will continue throughout the year.

In pointed remarks, Mr. Obama singled out states that have not expanded Medicaid to those making up to 138 percent of the federal poverty level — a key pillar of his law.

He said roughly half the states did not augment their programs “for no other reason than political spite.”

“That’s wrong. It should stop,” he said. “Those folks should be able to get health insurance like everybody else.”

But his remarks did little to ease the distrust between the White House and congressional Republicans. A number of Republicans are challenging the Census Bureau, which has switched the questions it asks about insurance coverage on its annual American Community Survey.

The survey is the main way the government keeps tabs on how many people have insurance, and Republican lawmakers say changing questions now will make it impossible to compare current enrollment with pre-Obamacare numbers.

Mr. Obama’s public remarks Thursday followed a private White House meeting with health insurance executives from across the country.

In attendance were 13 industry officials, including Karen Ignagni, CEO of America’s Health Insurance Plans, a leading trade group.

Vice President Joseph R. Biden and departing Health and Human Services Secretary Kathleen Sebelius also were there, as was Marilyn Tavenner, the administrator of the nation’s Medicare agency and most responsible for carrying out Obamacare.