With time ticking down to the end of open enrollment on Monday, the Obama Administration announced on Thursday afternoon that a late rush on healthcare.gov had pushed private health insurance signups over 6 million, pushing the White House over its revised enrollment goal.

"Amazing comeback story," tweeted White House senior adviser Dan Pfeiffer, who argued that in the wake of the terrible start for enrollment, that getting to 6 million would be 'impossible.'

The jump in signups seemed to be much like the rush we saw in December, when many Americans moved to get insured before the end of 2013, as officials said there were 1.5 million visits to healthcare.gov on Wednesday, with more than 430,000 calls into the insurance help call center.

The new signup numbers were relayed to health care activists during a conference call by President Obama, who spoke from Italy where he met earlier in the day with the Pope and Italian leaders.

"The President encouraged the navigators and volunteers to redouble their efforts over the next four days and leave no stone unturned in trying to bring affordable health coverage to as many Americans as possible by the March 31 deadline," a White House release said.

The White House was pulling every lever possible to get more people to sign up for the law, from trips by HHS Secretary Kathleen Sebelius to comedic posts on websites like BuzzFeed by Vice President Joe Biden's office.

"Making sure you've got affordable health insurance is a BFD," the Vice President's office tweeted, referring to Biden's off-color description of the plan as the President signed it into law just over four years ago.

"Outraged critics look for new reasons to oppose people getting covered," said White House Press Secretary Jay Carney in a mocking tweet from Italy, as he and other administration officials jabbed at Republican opposition to the health law.

The announcement of the 6 million figure came a day after the health law was buffeted by GOP criticism over the latest delay in enrollment, as the Obama Administration will allow people to finish their insurance applications after the March 31 deadline, if they started the paperwork by the signup deadline.