The official word from the priceline.com terms and conditions is:
Upon check-in, guests must present a valid ID and credit card or, in the hotel's discretion, debit card, in their name that is consistent with the transactional details provided to priceline.com (the amount of available credit required will vary by hotel). Debit cards may not be accepted.
Sounds like it was a good idea to call the hotels ahead of time and find out if they take debit cards and how much they would hold, as well as whether there are any alternatives (i.e. cash deposit, or posting no deposit but declining all "extra" services).