I think it's pretty standard at most banks, if you go over the amount your overdraft protection covers, you will acrue fees, causing your check to bounce. I think alot of people are confused on how this works.
Overdraft is only protection up to the amount specified. So if you have Overdraft protection up to $300, then that is all you are protected up to. So if you go over that $300 dollar limit by even 1 cent, you will be assessed for nsf for that 1 cent you are over, PLUS whatever the bank's fees are for nsf.
In your case, I'd do the math, and be sure to put whatever you'd be short into your account to make sure nothing bounces. Hopefully, you have some loose change around to make things balance out. If this car emergency messed up your budget, letting NSF fees kick in will really foul things up down the road for you, if you're thinking just sucking it up and letting the fees hit, or rolling with the punches is the way to go.
Otherwise, see if you can stop action on the rent check, and just pay it late this month to avoid bank fees. I find bank fees worse than anything. They gouge like crazy. They don't get rich for nothing.
At best, most apartments have a grace period for rent of about a week anyway. Any chance if you took advantage of this, you could find the money you are short somewhere else? Or at worst, call your landlord and maybe he'll cut you slack again.