To elaborate:
12 March
On March 12, in a hearing before Congress, Health and Human Services Secretary Kathleen Sebelius was asked whether the Obama administration would extend Obamacare’s open enrollment period beyond its scheduled close date of March 31. “No sir,” Sebelius responded, . . . UNDER OATH TO A CONGRESSMAN.
Later that day, a spokesperson for the Center for Medicare and Medicaid Services, expanded on that point. “We have no plans to extend the open enrollment period,” she said.
“In fact we don’t actually have the statutory authority to extend the open enrollment period in 2014.”25 March
The Obama administration has decided to give extra time to Americans who say that they are unable to enroll in health plans through the federal insurance marketplace by the March 31 deadline.
Federal officials confirmed Tuesday evening that all consumers who have begun to apply for coverage on HealthCare.gov, but who do not finish by Monday, will have until about mid-April to ask for an extension.

* * * EDITED TO ADD * * *
quote
[Speaker of the House John Boener responded] to the administration’s announcement on Tuesday evening that people who had begun the process of signing up for insurance through the federal exchanges would have until mid-April to do so, instead of March 31.
The Speaker mocked the use of the “honor system” to determine who was eligible for an extension after the administration said it would make no effort to ensure that people had actually begun the process of signing up by March 31.
endquote
Ref: The Hill