If it's the 16th that's 4 business days. But I agree, going through all the trouble of switching payment processors because you hope if the bank they're using fails they'll get back up and running in less than 4 days is a horrible ROI.
No payroll processor could have made payroll on time in this situation. If you overnight a letter from SF to NYC and the plane crashes on landing, the replacement letter is definitely going to be late.