WASHINGTON – New sign-up numbers are showing progress for President Barack Obama’s health care law, but not enough to guarantee that Americans who need coverage by New Year’s will be able to get it. That means more trouble for the White House after months of repairing a dysfunctional enrolmentwebsite.

Next year could start with a new round of political recriminations over the president’s signature domestic achievement: bringing the United States as close as it’s ever come to universal health care under the Affordable Care Act, Obamacare to its opponents.

Obama’s law uses a two-track approach to expand coverage for the uninsured. Middle-class people who don’t have access to job-based insurance can buy government-subsidized private plans. Low-income people are steered to an expanded version of the Medicare program for the poor in states accepting it, though not all do.

A website that went live on Oct. 1 is supposed to be the portal to both kinds of coverage, but technical problems turned it into a frustrating bottleneck for millions of consumers. That has fueled Republican arguments against the 3-year-old health law, which they have tried repeatedly to repeal.

Enrolment statistics for the plan showed that 364,682 people have signed up for private coverage as of Nov. 30. Although that’s more than three times the October total, it’s less than one-third of the 1.2 million people officials had originally projected would enrol nationwide by the end of November.

Crunch time is now, as people face a Dec. 23 deadline to sign up if they are to have coverage by Jan. 1.

The website problems have created stress and uncertainty not only for the uninsured but also for other people who now have insurance but are seeking to avoid an interruption in coverage in January.

Those who are trying to preserve their coverage include some of the more than 4 million people whose individual plans were cancelled because they didn’t measure up under the law — as well as hundreds of thousands who are in federal and state programs for people with serious health problems, from cancer to heart disease to AIDS.

Health and Human Services Secretary Kathleen Sebelius said in a blog post early Wednesday that she is asking the department’s inspector general to investigate the contracting process, management, performance and payment issues that may have contributed to the flawed launch of HealthCare.gov.

But she told the House Energy and Commerce committee later Wednesday that the signup trend is turning positive.

Lawmakers want explanations for dozens of questions about the website’s design, workability and security. They also want to know why Sebelius and other top officials repeatedly assured them everything was on track.

Democratic lawmakers, who are worried that the fiasco will hurt the party in congressional elections next year, say they are relieved the website is finally working. But some are not convinced the turnaround is complete.

“How confident I am? I’m hoping that we’re moving in the right direction,” said Rep. Eliot Engel, a New York Democrat, after Wednesday’s Energy and Commerce Committee hearing. “And if we find the day has come and we find that it’s not what we had hoped, then I think there should be changes.”

Republicans have called for the resignation of Sebelius. Even some Democrats have urged Obama to fire those responsible, but the White House has given no indication that a house-cleaning is coming. Instead, it has brought in outside management to help Sebelius and her department cope.

The secretary’s unusual pre-dawn announcement of an inspector general probe indicates that she realizes she has some explaining to do.

Sebelius said at least 1.9 million people appear to be waiting just offstage to sign up. They’ve been found eligible to enrol but haven’t yet picked a plan.

If they’re all procrastinators who rush forward on Dec. 23, the website would be overwhelmed. It can only handle 50,000 people at a time.

Nationally, an additional 803,077 people have been determined to be eligible for Medicaid, the safety-net program shaping up as the health overhaul’s early success story. That’s about double the number for October. Nonetheless, state Medicaid directors are reporting accuracy problems with information on prospective enrollees that the federal government is sending them.

The administration had spent $677 million on website technology through the end of October, aiming for smoother operations, but with results still well short of perfection.