This is a good question. I am worried about this too. I am in California and checked out coveredca.com/FAQs/ and saw this:
"However, some individuals may be exempt from paying a penalty, including:
people who would have to pay more than 8 percent of their income for health insurance
people with incomes below the threshold required for filing taxes (in 2013, $9,750 for a single person and $27,100 for a married couple with two children)
people who qualify for religious exemptions
undocumented immigrants
incarcerated individuals
members of federally recognized American Indian tribes and Alaska Natives"
I also gave a call to them (1800-300-1506) and they said that I did not qualify to get health care coverage and would not get fined when I filed taxes. I'm not sure if this is the same in all states. I suggest (if you live in Cali), you give them a call for your peace of mind. There will be a long wait period, but it's best to wait than to have to deal with an unexpected fine.