Just went to Bank of America, met with the person who assists with accounts being opened. Explained our case - why you want to open an account, why you don't have a Social Security number and show identification (passport). Wachovia Bank would not open an account for us and a few other banks would not either. Bank of America are the bank that allow illegal mexican immigrants get a credit card with them this is a market that is worth millions.
By the way it is not illegal for a non-american resident to have a bank account but the bank workers are meant to verify who you are, get to know you, etc. This is under the Patriot Act which is meant to prevent terrorists opening bank accounts.