The banks I've talked with want the SSN of someone who can qualify for a revolving line of credit equal to your transaction volume. ie, you want to do 30K of money per month, you have to be wealthy enough to swing a $30,000 unsecured bank loan. The "reserve balance" thing is no longer being offered.
The standard is to require a signature (or two) of a guarantor. I don't think they actually check the guarantor's bank account or credit limit though. That said I've only gone to dedicated merchants, and not banks.