If your termination was in any way a violation of an employment contract that you had with the employer, you might have something and would need to file at once for unemployment benefits and then see an attorney who specializes in employment issues.
If you believe the termination was in violation of one of the EEOC regulations, in other words if you feel that your employer was behaving in a discriminatory way toward you based upon your sex, religious affiliation, race, etc. then this might be something that could make the termination questionable. If this were so, you'd file at once for unemployment benefits if you haven't done so already and then take the situation up with the EEOC.
If you were asked to do something illegal, immoral or particularly unsafe, or were asked to cover up wrongdoing or knew of something going on that was unsafe or illegal, and were terminated for your refusal to do so, there might be a slight possibility of an issue. You'd file for unemployment benefits and then possibly talk to an attorney. If you were fired in violation of the ADA, had made your employer aware of a disability and were terminated as a result of it, there might be something there.
Otherwise, probably there won't be any grounds to see someone, no wrongful termination involved. Because whether or not they did it fairly or justly or honestly or nicely, it's pretty much an at will state, as you said. But the unemployment insurance situation is where you'd have some recourse.
Because if they terminate you, and you have monetary eligibility to draw unemployment insurance, the employer must show that they had a good, valid misconduct reason to terminate you to keep you from receiving your unemployment benefits which will cause their tax rates to go up. In fact, even if you were to have any other kind of case, the first thing the attorney would probably advise you to do is file for your unemployment benefits while you are sorting out this other issue, which might take a long time, even if you were to prevail and show they terminated you wrongfully in some manner. Filing for benefits shakes the employer into giving some reason, for providing proof of your misconduct if they have any, or else they roll and say you were let go for lack of work or otherwise choose not to appeal the claim for benefits. Either way, it helps clarify what they're going to say in the future regarding your termination, and if they are determined not to have had a valid reason, it gives you some extra income to live on while you are job searching, having been put out of work through no fault of your own.
When you file your claim for unemployment you will tell the reason that you were terminated, describe what happened and what you were told by the employer. Then the unemployment system will contact the employer and ask them for the exact circumstances, why they say you were terminated. Neither you nor the employer is able to decide whether you get the benefits or not, this decision is made by the agency following the unemployment statutes and determining whether the employer can show they did have a valid misconduct reason to terminate you. Being sick, incidentally, even to the point of violating attendance policies and being terminated for this is not considered misconduct (for unemployment insurance purposes)if you had a valid documented medical excuse.
You file your claim for unemployment benefits. It will take some time to sort out the situation and get a decision on your eligibility. In the meantime you're looking for other work. The unemployment insurance is not needs based, it is not given only to those who are impoverished or really need it, so file immediately if you haven't already, even if you expect to find another job very shortly.
