Can I ask Bank of America to allow me to overdraw my account if I'm willing to pay the fees?

I have an unforeseen expense this month that needs to be paid ASAP and my check will not deposit into my account until Thursday. I am willing to pay any fees necessary. Basically I did not realize that since a new year is starting on my water bill, they charge a $100 fee or shut your water off because they assume that you do not want the account anymore. I have already requested an extension once trying to get to this Thursday. The check that will be deposited on Thursday is $270, so plenty to cover it. I called and 'chatted' with a customer service representative on their website and she pretty much said that there is nothing that they can do. Would I get a different response if I call & speak to someone?

I know that this is extremely irresponsible of me, but sometimes things happen. I'm kicking myself for forgetting about this fee. Anyone have any additional ideas?