Will US 2 dollar bills ever be worth more than 2 dollars?

Modern ones are unlikely to go up in value anytime soon. Even though $2 notes only make up about 1% of all bills in circulation that still amounts to hundreds of millions of them. They're uncommon, but they're not rare.

On the other hand, older ones (1928 and earlier) are already worth more than face value because they're of interest to collectors.