If you are limiting your expenses to not draw attention and don't advertise the cache there is no limit. This, of course, assumes that normal household bills are paid in credit/bank debits. Just don't opt for automatic withdrawals and insist on authorizing each.

I use a credit card as a buffer between bill payments and bank deposits so I am in control of each, and a late payment on a credit card is much less damaging to one's credit than a bunch of them for each bill one deals with normally.

In a worst-case scenario doing this could enable one to continue service from many providers for months before the credit card was cut off. Just don't use your deposit bank as your credit card provider. They usually have lousy rates anyway.