As of 1:15 pm EST HealthCare.gov gives you this error message:

According to Valerie Jarrett, Obama is in the process of enrolling today:

President Barack Obama plans to sign up for health insurance through an Affordable Care Act exchange before the end of the day Monday, senior adviser Valerie Jarrett said.

Jarrett made the announcement in an interview with April Ryan of American Urban Radio Networks, apparently ahead of the White House’s planned rollout. Officials did not respond to repeated requests for confirmation.

The White House first said in 2010 that the president, who has coverage through the federal government and gets his care from White House doctors, would sign up for insurance through an exchange.

Update: Right as the website crashes the White House says he enrolled. Timing seems just a tad suspect IMO.