Well, they need to be Citizen or PR for sure. when you do joint sponser, basically they take all responsibility for that immigrant (in case is your spouse). Usllay if you are not Citizen or PR even bank doesn't approve you for any loans.
Work papers doesn't really mean legal or illegal, depends on the status they have thru immigration.
I know people in San Diego which have work documents and file taxes but they are not legal nor illegal.. it is hard to say unless they guys tell you the truth about their status. (My wife has ITIN number but she is not here, she files tax with me but she has no status in the United States, she is not legal or illegal but she can not be a joint sponser)
For you to bring your spouse here, I wouldn't do anything crazy like this. Embassies are really picky and even people have the right paper work they get picked on.
It is hard for you probably in this situation to find what to do, but if I were you I wouldn't do anything stupid specially on my Spouse's case and find someone with solid status and decent income to support yo.
Good Luck