WASHINGTON — With time running short, the nation’s health care rolls still aren’t filling up fast enough.

New sign-up numbers Wednesday showed progress for President Barack Obama’s health care law, but not enough to guarantee that Americans who want and need coverage by Jan. 1 will be able to get it. Crunch time is now, as people face a Dec. 23 deadline to sign up if they are to have coverage by New Year’s.

That means more trouble for the White House, too, after months of repairing a dysfunctional enrollment website. Next year could start with a new round of political recriminations over the Affordable Care Act, “Obama-Care” to its opponents.

The Health and Human Services Department reported that 364,682 people had signed up for private coverage under the law as of Nov. 30. That is more than three times the October figure, but still less than one-third of the 1.2 million that officials had projected would enroll nationwide by the end of November. The administration’s overall goal was to sign up 7 million people by next March 31.

Secretary Kathleen Sebelius assured Congress on Wednesday that “we are seeing very, very positive trends” now that HealthCare.gov is working reasonably well. She also announced she’d asked the department’s inspector general for an independent investigation into contracting and management factors that contributed to the technology failure.