If I was told that I was laid off due to budget cuts but there were in fact no such cuts, do I have a case?

Unfortunately, you most likely would not have a case. If you have an employment contract which protects your employment in some way (such as by limiting for reasons for termination), you may enforce that contract. However, without an employment contract, you are an employee at will, and may be terminated at any time, for any reason. Moreover, the law does not require the employer to explain the reason for termination, so it does not matter what the employer said in this regards--even if it is untrue (which could, theoretically, have been done for compassionate reasons; e.g. maybe the company didn't want to tell you that you weren't working out for some reason), that does not give you any claim or cause of action.

So, if you are an employee at will, it does not matter whether there were or were not budget cuts--your employer could terminate you.

The exception is that termination for certain specified grounds is prohibited. If you feel that the true reason for your termination was one of the following, consult with an employment law attorney--you may have a legal claim:

1) Illegal discrimination: under federal law, an employer may not terminate someone due to his/her race, sex, religion, age over 40, or disabiltiy; some states protect a few other categories, like sexual orientation or national origin.

2) Illegal retaliation: it is against the law to fire someone for using a specifically protected benefit, like taking FMLA leave, or making certain protected complaints or claims, such as for overtime or that you were discriminated against.