I currently do not have health coverage and I am being claimed as a dependent by a family member. They were recently informed that would have to pay the penalty for my lack of health care insurance. I really don't wish to burden them with this obligation. Is there any way that I can pay the penalty on future tax returns being that I did not do one this year because of no income?

I currently do not have health coverage and I am being claimed as a dependent by a family member. They were recently informed that would have to pay the penalty for my lack of health care insurance.========>Correct; beginning in 2014, you , a dependent, would not be penalized, the person claiming you as a dependent gets penalized , called shared responsibility payment ,for not having insurance for you, a dependent listed on their return.

I really don't wish to burden them with this obligation. Is there any way that I can pay the penalty on future tax returns being that I did not do one this year because of no income?======>They must pay a fine to the government ; even if the they are exempt from the ACA penalty, they can still be fined for not having insurance for a dependent/ their children.