March 27 (Bloomberg) — Six million Americans have signed up for private health plans under Obamacare, President Barack Obama said today, a symbolic milestone for a government that has struggled to get the law off the ground.

Obama announced reaching the mark on a conference call today with thousands of workers who had helped enroll people, according to an e-mail the White House sent to reporters. The president encouraged the workers in the call "to redouble their efforts over the next four days" before March 31, the deadline when Americans must have started the application process or face a fine of up to 1 percent of their income.

Nearly four million people have visited healthcare.gov, the federal enrollment website, since Monday and hundreds of thousands of people have phoned government call centers in advance of the deadline, officials said. States running their own enrollment systems under the Patient Protection and Affordable Care Act have reported a similar surge.