I think you are just playing with fire. Sure, it can work for years, but as others have said, one screwup with your deposit and you are up a creek with no way of knowing or time to fix it. If you schedule it the next day, then you can always scrounge up some cash (friends/relatives/etc) and deposit it the next day if you see there is an error in time to pay your bill.
I personally think people need a small buffer anyways. For me, I keep $100 in checking more than I ever need. True, mathematically I should invest that. But even if I could get a 10% return on my stocks, that $100 buffer only costs me 83 cents a month. If I royally screw up or if my bank/employer royaly screws up, that $100 will cover most bills (electricity, gas, water, insurance, student loan, garbage, etc are almost always under that $100 a month for me). If everyone set this buffer up, they'd all save a LOT of headaches, and the question of yours would be nearly irrelevant.
Also, a majority of companies are flexible with due dates. I have set almost all of my bills (utilities and credit cards) to be due 10 days after my paycheck is deposited. Only two companies refused to change the due date for me and one of those was due 15 days after my paycheck and it wasn't worth fighting to move it just 5 days. That 10 days gives me a few days buffer after my paycheck is depostited and a few days buffer to make certain that my bill payment went through. On either side, I have time to fix any problems.