I paid one card over the phone literally 5 minutes late, so I called up Customer Service and asked what they could do for me. Their answer was more or less, "Tough shit, take the $35 assram and like it." I cancelled the card that very minute. Having good credit rocks.
As for what will happen to your rating, I don't know it's still like this, but back in the mid-90's, I was told that your payments records are tracked 0-30 days late, 31-60 days late, 61-90 days late, etc... So a 3-4 day late payment gets recorded the same as an on-time (or 29 days late) payment, but you still get the late fee and interest charges. Check your credit agreement too, one late payment might be enough for them to jack up your interest rate.