There can be different rules for Debit vs credit card purchases. Like some rental car companie will take a debit and some wont. At least that used to be the way. Some hotels charge the whole bill upfront on your debit and some wont. You can always negotiate with the manager and be extra nice and sometimes they wont. Generally if you have kids in tow, they will, so approach the desk alone, clean, and bright and be articulate. Explain that you are on an extremely limited amount of funds, and if he attachs your debit card, you wont be able to buy trinkets for the family you came to visit. Most are compassionate.

Btw, please negotiate your rate. Roomsaver.com has awesome coupons that can be used if you walk in that day and want a room. You can get a $120 room for $49. If you need to make a reservation use places like hotels.com or the like. You can always speak to the manager and ask for if they have any "managers specials available" its generally a room that is obstructed view, or near construction or smaller and has double beds, not the lush king sized bed. They generally give those rooms out for half price or less.

Good luck with your journey.