Mary, same here - credit card issuers, all of them or most do schedule the due date during the weekends, and they do not process payments on weekends (or legal holidays). It is a sham, and if they not sued for that yet, they'd be some day.
Given that, we're better off knowing their rules and playing by them. The late fee of $29/$35 are the major profit center for all the banks, and the float for an extra day for you is most likely zero these days. I don't advocate paying bills earlier, nor I ever use the "autopay" feature, it just makes sense to follow their rules.
If you insist on "pushing" funds from our bank to payees, you favorite bank will not stand by you unless you sent the payment 5 days in advance, though mostly payments get there sooner then that.
When you "pull" money by using credit card issuer's payment system, you always guaranteed the posting date, I quote from First Usa:
"It will take up to 3 business days for your payment to post to your account. Please make sure the date you enter for the payment is at least 3 business days before your payment due date."
True, that's the longest delay among the majors - but it is reliable. For instance, Amex posts the payment on the same day you schedule it - and pull them from the checking two-three days later.