I'd read earlier on that after you pay your bill once with a debit card, you can do it without speaking to a rep. I was actually able to do it on the phone for the first time without speaking to a rep at all.
It went something like this:
Automated Prompt: "Blah Blah What would you like help with today?"
My initial voice option: "Make payment"
Automated prompt: "Blah blah blah *some time later* speak or enter your checking account number"
Me: Press # and 0 a bunch of times to try to transfer to a rep
Prompt: "I'm having trouble collecting your checking account number. Would you like to pay with a debit card?"
Me, internally: "Why yes, yes I would."