Drilling it out would be a last resort.
You didn't say what year your Aveo is. On mine (2009) the box is plastic and the screws have a Philips head. The problem with drilling out the screw is that if it is stripped, it may turn itself while you are drilling it. Also, it's a metal screw into plastic - I don't recall whether the box has a threaded metal insert or whether it is threaded directly into the plastic of the box itself.
Try this: Using a small set of Vise-grip pliers, lock onto the screw head. Pull upward on the screw, exerting pressure as you turn it.