you do get a grace period and its longer than 2 days, but i would call them and just let sprint know it will be late. they are also good about setting up a payment arrangement if you ever need it; thats one good thing i can say about sprint, i'd had times when i couldnt pay the whole bill and they will work with you most of the time.
Paying the bill late can also result in a late payment fee on your next bill. All if your bill is due it would make a difference if you are carrying a balance forward for last month or a currently under a payment arrangement.
There is a 10 day grace period from the bill due date. You can also contact customer service and make payment arrangements if you see it's going to go past the 10 days.