WASHINGTON (AP) — More than 11 million people signed up for subsidized private health insurance under President Barack Obama's law this year, the White House announced Tuesday evening.

But that preliminary estimate — 11.4 million people — comes with a couple of asterisks:

—The final number could grow because the administration is offering a grace period for people who started applications — but couldn't finish them — before last Sunday's official deadline. They have until February 22, this coming Sunday.

Also, Democratic lawmakers are pressing Obama to grant a second chance to sign up for uninsured people facing tax penalties.

—The final number could shrink if consumers who've enrolled for 2015 coverage don't follow through by paying their share of premiums.

"The Affordable Care Act is working," Obama said in a White House video. "It's working a little better than we anticipated. Certainly, I think, working a lot better than many of the critics talked about early on."

Last year, 8 million people had initially signed up. But by fall, just 6.7 million were still in the program. Some of those who left found other coverage, through a job for example.

According to independent studies, at least 10 million uninsured people gained coverage last year as the health care law's big insurance expansion got under way. One part of the law offers subsidized private health insurance tailored to workers and families who don't have coverage on the job. Another part expands Medicaid to serve low-income adults in states that accept it.

The nonpartisan Congressional Budget Office estimates that this year there will be 19 million fewer uninsured Americans than if the law had never passed.

Sign-up season for private plans went relatively smoothly this year, a turnaround from the technology meltdown that embarrassed the White House last year. Coverage is offered through online health insurance markets, also called exchanges. The federal HealthCare.gov website serves 37 states, while the rest run their own markets.

Although HealthCare.gov was slowed by a glitch on Saturday, an independent assessment for The Associated Press found that the website worked smoothly overall during its big weekend.

Catchpoint Systems, which monitors website performance, found that HealthCare.gov's sign-up page was available more than 99 percent of the time from last Friday through Sunday, and typically loaded in about 4 seconds.

Catchpoint CEO Mehdi Daoudi called that "very good."

Separately, privacy concerns have been raised about HealthCare.gov this year, after The Associated Press reported that the site was quietly sending some personal consumer information to companies that specialize in analyzing Internet data for performance and marketing. The administration quickly scaled back the practice, but there's an ongoing congressional inquiry into the matter.

This biggest question hanging over HealthCare.gov this year has nothing to do with technology.

Early next month, the Supreme Court will hear arguments on another challenge to Obama's law. The plaintiffs in the case say the literal text of the legislation only allows the federal government to offer subsidies in states that set up their own insurance markets. Most states have not done so.

If the court sides with the plaintiffs, millions of people would lose financial assistance, and most of those would drop their coverage.