Some states are already gaming the Obamacare enrollment deadline by announcing that those who start the sign-up process by the official deadline of March 31 can have extra time to complete their applications.

Maryland, Nevada and Minnesota have already announced the wiggle room. Minnesota officials also said that so long as the late-signers have coverage kicking in by May 1, they will not be subject to a fine for lacking health insurance. This was later confirmed as acceptable by the Department of Health and Human Services (HHS).

Under the Affordable Care Act (ACA), Americans who lack health insurance for 90 days or more in 2014 can be fined $95, or 1 percent of their income, prorated for the period they lacked coverage, though the government has offered many "hardship" exemptions. The fine is set to rise each year.

Oregon, whose online Health Care Marketplace is still not fully operational, is considering an outright extension of the sign-up deadline, something that would require approval from the federal government.