(Photo by Win McNamee/Getty Images)

About 11.4 million Americans have signed up for private health insurance coverage through Obamacare exchanges by the official end of the law's second-ever enrollment period, the White House announced in a video Tuesday night.

The announcement indicates the Obama administration will beat its own 2015 enrollment goals after a much quieter sign-up season this year. But the announcement also comes just weeks before the Supreme Court will hear a case challenging the legality of premium subsidies provided through the nearly three dozen states relying on HealthCare.gov for enrollment.

The number of enrollments will likely drop throughout the year. For instance, 8 million people had signed up for exchange coverage when the law's first-ever enrollment period ended in April 2014, but by November, 6.7 million remained enrolled in exchange plans. The administration said last fall it hoped to keep at least 9.1 million enrolled in exchange coverage throughout 2015, a target that now seems likely secure. Still, the nonpartisan Congressional Budget Office had projected 12 million people would be enrolled in 2015 exchange coverage.

"The Affordable Care Act is working," Obama said in the White House video released Monday night. "It's working a little better than we expected."

Though the enrollment window officially closed on Feb. 15, the administration is keeping it open through this Sunday for people who started an application before the deadline. Most states running their own exchanges are also allowing some enrollment leeway.

The administration has also said it's considering a special enrollment period for uninsured people who'll find out this tax season they have to pay the individual mandate penalty for not having coverage. The administration expects up to 6 million will face this penalty, which starts at $95 or 1 percent of household income in 2014. The minimum penalty in 2015 more than triples to $325, or 2 percent of income.

Oral arguments in King v. Burwell, the Supreme Court case challenging the premium subsidies, are scheduled for March 4, with a decision expected in late June. More than 8 in 10 people purchasing coverage through the exchanges received subsidies, worth on average three-fourths of monthly premiums.