It will rarely take the full 30 days and should be complete with the 2 weeks. However, they give you that disclosure so you know you might have to make some payments to your other lender to avoid late fees.
Can you check your Nat'l City account online? How long do your online payments usually take to post? You can also, usually, pay via phone the day before the account is due if it still hasn't cleared. Nat'l City may charge you a fee for this