President Obama said Thursday that "close to 4 million Americans" had signed up for insurance on the ObamaCare exchanges, a hint that enrollments might be accelerating as the deadline to purchase coverage nears.

Last Wednesday, the Obama administration said just under 3.3 million Americans had purchased plans since Oct. 1 through exchanges created by the Affordable Care Act (ACA).

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"Right now, we've already got close to 4 million Americans who signed up for exchanges," Obama told a gathering of Democratic donors and governors at a luxury hotel just blocks from the White House.

The president said, despite the botched rollout of the ObamaCare website, more than 10 million people now knew financial security because they had obtained coverage via the federal exchanges, Medicaid expansion or the ACA provision allowing young adults to stay on their parents' insurance for longer.

Obama's optimism came just a day after Vice President Biden acknowledged a "shaky" rollout of the law and said the administration might miss its enrollment targets.

"We may not get to 7 million; we may get to five or six, but that's a hell of a start," Biden said.

Consumers must purchase coverage before March 31 or wait until the enrollment period reopens toward the end of the year.

At the White House earlier Thursday, spokesman Josh Earnest said reports earlier in the week that some localities — including California — were exceeding their enrollment goals was evidence that problems with the ObamaCare website had been ironed out.

"One, it indicates that the healthcare website that was the subject of so much consternation and frustration both from this administration, but also from people across the country who were trying to use it, that a lot of those problems have been resolved, and that we have a website that's functioning pretty well," Earnest sad.

"The second thing it indicates is that that functioning website is presenting options to people who visit it that are attractive; that people are looking on that website, finding that there are healthcare options that previously weren’t available to their family; that these are healthcare offerings that are of a higher quality and a lower cost than was previously available," he continued. "They're taking advantage of that opportunity by signing up, and that's why we’re seeing those strong numbers."