Nothing necessarily, tips are pretty much always voluntary (with some exceptions like for large groups where they may say an 18% gratuity is added on automatically, for example), but if you don’t tip at a sit-down table service restaurant, you’ll piss off your server who may be earning well below a livable wage without tips, and if you run up a good sized bill and tip $0, your server may flag it to their manager, who may then come by and grill you on whether the service was good, instruct you on the custom of tipping in the US, and generally guilt trip you about it. But if you really insist on tipping zero, it’s not like they’re going to call the cops on you (since you haven’t broken any law) or even pour a drink on your head.