WASHINGTON — Seeking to regroup from his healthcare law’s disastrous rollout, President Barack Obama on Tuesday insisted that the sweeping overhaul is working and warned Republican critics that he would fight any efforts to strip away its protections.

“We’re not repealing it as long as I’m president,” Obama said during a health care event at the White House. “If I have to fight another three years to make sure this law works, then that’s what I’ll do.”

Earlier Tuesday, the administration released a 50-state report saying that nearly 1.5 million people were found eligible for Medicaid during October. As website problems depressed sign-ups for subsidized private coverage, that safety-net program for low-income people saw a nearly 16 percent increase in states that have agreed to expand it, according to the Department of Health and Human Services.

The White House is trying to cast the health care law in a positive light after the first two months of enrollment for the centerpiece insurance exchanges were marred with technical problems. With the majority of problems with the sign-up website resolved, by the accounting of administration officials, Obama and his team plan to spend much of December trying to remind Americans why the administration fought for the law in the first place.

“We believe that in America, nobody should have to worry about going broke because somebody in their family or they got sick,” Obama said, flanked by people the White House says have benefited from the law.

Despite Obama’s sunny presentation, officials are furiously working behind the scenes to rectify an unresolved issue with enrollment data that could become a significant headache after the first of the year. Insurers say much of the enrollment data they’re receiving is practically useless, meaning some consumers might not be able to get access to benefits on Jan. 1, the date their coverage is scheduled to take effect.

On Monday, administration officials and insurance company representatives began holding daily 7 a.m. meetings to discuss the enrollment data. Officials at the Centers for Medicaid and Medicare Services — the department overseeing the insurance exchanges — are also personally reaching out to some individuals who have enrolled online to make sure their information is correct and that they are sending payments. Call center representatives are doing the same with some people who enrolled over the phone.