WASHINGTON — The Obama administration said Tuesday it’s making steady progress on health care sign-ups, but the White House needs something close to a miracle to meet its goal of enrolling 6 million people by the end of this month.

It could happen with a sustained surge in consumer demand and a foolproof website. But they’re not seeing it yet, and time is running out.

The Department of Health and Human Services said more than 940,000 people signed up during February for private coverage under President Barack Obama’s health care law, bringing total sign-ups to 4.2 million.

With open enrollment ending March 31, that means to meet the goal, another 1.8 million people would have to sign up during the month, an average of about 60,000 a day.

That’s way above the daily averages for January and February, which have ranged between 33,000 and 34,000. The math seems to be going against the administration.

If the target isn’t met, the immediate fallout will be political. Republicans will say it proves their point that Obama’s signature project never had the public’s support. Backers of the law will have to work harder to smooth out some of its problems and convince Americans to take a second look.

Administration officials expect the pace to pick up as procrastinators are forced to act. There are no plans to extend the March 31 deadline, they emphasize. The big question is whether that will be enough to make up for the technical troubles that paralyzed HealthCare.gov much of last fall and the continuing challenges for several state-sponsored websites.

“Given what we know about past enrollment patterns for health care, we expect that even more (people) will sign up as we approach the March 31 deadline,” said HHS Secretary Kathleen Sebelius.

Julie Bataille, communications director for the health care rollout, said she expects millions more to sign up – but she wouldn’t commit to a number by March 31.

The goal of 6 million sign-ups is itself a lower bar than was originally set. The Congressional Budget Office scaled back its original target of 7 million because of the federal website’s computer problems. HealthCare.gov serves 36 states, while 14 states and Washington, D.C., are running their own sites.

The 943,000 enrolled in February fell short of the target of 1.27 million that HHS had initially set for the month.

And the cumulative total of 4.2 million sign-ups is just three-fourths of the 5.65 million that HHS originally projected would sign up by the end of February. Those estimates are from a Sept. 5, 2013 departmental memo.

The numbers released Tuesday still don’t say how many of those signing up were previously uninsured, which is the ultimate test of Obama’s health care overhaul.

And they don’t say how many consumers have sealed the deal by paying their premiums.

Health care industry consultant Robert Laszewski said that undercuts his confidence in the numbers.

“They are still reporting numbers that are inflated,” he said.