Actually, there are number of websites, most of which want you to subscribe to their genealogical services. They all use the same database, and they mostly suck.
The one and only database is put out by the SSA. Everybody on it is supposed to be dead. The SSNs of the dead people are a matter of public record, and, obviously, invalid for use, by, say, a fry cook or a president.
You can go to that site, pick a number, and poof you have a new number for a new identity.
Until somebody looks up your supposed SSN on that database. Then, poof, you big loser!
In a time where lawlessness did not reign that would probably happen. But today many people are using number(s) like Obama is and nobody does nothin.'