Like all Federal Reserve Notes (FRNs, aka "bills" or "cash"), the $2 FRN is "legal tender for all debts, public and private."
However, a lot of people don't know about them. If I owe someone $10, and all I have is five $2 bills, is it legal for him to refuse to accept them because he's sure that $2 bills don't exist and they must be counterfeit? Assume that for some reason, he can't just Google "$2 bill" and see that they're real.