Sen. Jeanne Shaheen, D-N.H., urged President Obama in a letter to consider extending the open enrollment period for Obamacare beyond March 31, 2014, given the IT problems confronting the program.

But that decision isn't up to Obama.

Even if Obama wanted to extend the open enrollment period, he wouldn't be allowed to without an act of Congress — at least if he wants to follow the law he signed.

Though the health care law granted the Secretary of Health and Human Services discretion to define dates for the open enrollment period to occur each year, it also specified that the initial enrollment period (i.e. the current one) had to be announced by July 1, 2012.

Specifically, Section 1311 of the healthcare law reads, "ENROLLMENT PERIODS: The Secretary shall require an Exchange to provide for-- (A) an initial open enrollment, as determined by the Secretary (such determination to be made not later than July 1, 2012)."

Given that HHS Secretary Kathleen Sebelius has already determined that the enrollment period must end on March 31 — and nearly 16 months has passed since she made that determination — extending the period would require an act of Congress to change the law.