I take it you want not just a debit card, but a debit card attached to an American Bank account, correct?

Getting the bank account may be modest hurdle. If you will be a resident alien, it should be easy enough to get an account at any number of banks provided you bring proper ID (passport, green card, et cetera as may apply to you). Most anyone who can obtain a checking account will find it easy to get a debit card attached to it.

If you simply visiting, your options are much more limited.

It would help to know just want you want to a debit card for. If you're only visiting and want a convenient means of payment, traveler's checks may be a good option.