The company certainly can fire you. While it probably could sue you for fraud, it would almost never be worth their while to do so. They probably also could refuse to have you work on their project. If your concern is that unless you keep lying, they will find you out, you should seek advice from an employment lawyer in your state in terms of the consequences. You're squarely in a "tangled web"--I hope you find a way out which will allow you to sleep at night. Good luck.