I was terminated on December 31 2010 was told my health insurance was terminated on that day I did not receive a letter until jan 3 2011 can they do this

Yes, of course they can.
Letters are NOT instant.

Can they terminate your insurance effective the same day as your employment ends? Yes (generally the end of a calendar month).
Can they send you a letter that day which you received 3 days later? Yes.
Are you wondering if they have to notify you in advance that insurance was going to end? No.
In the US you can pay for COBRA insurance after employment ends, but only if the employer qualified for the plan, and although cheaper than some plans, it still isn't cheap. If your employer had <20 employees he probably didn't have it, and there is no law that they have to have it; it just costs them more to not have it.
Many states have a plan that you can pay for too. Check your state.gov website.