OK, let's try this one more time. Again.
A month after Obamacare's open enrollment season closed, the federal government Sunday starts a special enrollment period for people who only now are finding out they face a penalty for failing to have obtained some form of health insurance in 2014.
"We clearly are very hopeful that people will avail themselves of the chance to get covered, to get insurance during this period," said Kevin Counihan, CEO of HealthCare.gov, the federal Obamacare insurance marketplace that serves 37 states.
But it's unclear how many people will take advantage of that offer and end up adding to the 11.7 million people or so who already signed up for 2015 health plans on government Obamacare exchanges.
"We haven't set a projection," Sylvia Burwell, secretary of the U.S. Department Health and Human Services, said Thursday when CNBC.com asked her about the number of sign-ups she expected to see, during an event at Montefiore Medical Center in New York.
A survey released Monday by the Jackson Hewitt Tax Service suggested that many eligible people might not even know about the offer of what will amount to their third bite at the Obamacare enrollment apple.
The study found that 48 percent of adults believed the deadline to sign up for health coverage this year had expired, and another 27 percent "don't know" if the deadline had expired. While open enrollment for Obamacare insurance ended in most of the country on Feb. 15, special enrollment periods for tax season were announced in the week following that initial deadline.
Read MoreObamacare-canceled plans fell in2015