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Having been a paralegal and written an entire memorandum on the subject, I can tell you if you are considered an employee-at-will (which most employees are), you will have no recourse, unless there is discrimination involved. For that to happen, you would have to reside in what current law refers to as a "protected class", most notably African Americans and Women. Essentially an employer can dismiss for just about any reason if you are an employee-at-will, with obvious exceptions.
If you have an employment contract or the employer publishes an employee handbook, they are required by law to dismiss you according to any procedures outlined in either the contract or the handbook. If either of these two scenarios are present in your case, you may have good cause to bring a lawsuit.
If I were you, I would apply for unemployment benefits. It may take a month or so but it's likely from you've said you will be able to prove to the adjudicator that your firing was unjust (the above law I mentioned does not come into play with respect to an unemployment claim as they are an entirely separate ageny unto themselves with their own regulatory requirements).
Sorry, I don't mean to be pessimistic about it. Just do a search on employee at will on google and you should be able to confirm what I have told you. If you have enough previous work though, you should be able to obtain unemployment benefits. I would suggest filing your claim immediately as you while your case is being considered, you still file you weekly claims and if it's decided in your favor, they send you a check for all the weeks you filed while waiting for your claim to be adjudicated.