After four, but if you want to keep a second day draft pick around, you're going to either have to give him a higher tender than he might be worth (did we end up giving Leckey a second-round tender?), or you risk losing him (like when the Saints nabbed Jason David from the Colts) or having to pay more than you expected or wanted to (like Reggie Wells two years ago).
Part of the argument is that not giving four-year deals to all your rookies means that you likely expect these guys to fail (since you don't want to spread cap money over 4 years) or that you're trying to save money this year at the expense of a possible developed player in four years (because a minimum-salary contract in year 4 will be less expensive than a high tender).
Second-day rookies don't really have any leverage. If the deal is slotted, they basically have to take what they're offered. By not signing guys for four years, the Cards are saving a couple grand on the front end, but gambling that their players develop, but don't develop that much. I think that's the definition of penny wise and pound foolish.
How many restricted FAs didn't sign with their original teams this year?