I'm more familiar with the rental car world than the hotel world, but note that at least some hotels and definitely many rental car locations won't even accept a debit card for a deposit (statistically, those who don't have credit cards tend to be riskier/more problematic customers--obviously not the case in your situation, but policies are policies). Be sure that whichever hotel you stay at will (and if they require extra qualification steps, such as flight itineraries or a check of your credit history, that you'll be able to supply or pass those--a foreign student without a U.S. credit history probably wouldn't pass a credit check).

And deposit amounts vary HEAVILY between locations, so you'd really need to check with the specific hotel. Of course, that's rather hard to do when using an opaque site like PL until it's too late...