Hmm I don't actually know what would happen if we as a couple applied for gov't aid. I don't see how that would ever be possible though, a family of 3 needs to make less than 2k a month.
The premise I understand is if say we got divorced and say in 10 years she applied for some welfare (again unlikely since I'm sure she'd be getting plenty of $ still from me :( ) I would be on the hook for it as I sponsored her visa into this country. Every visa given to family member to enter the usa has to be sponsored by someone making ~2x the povery level that guarantees that they will not become a receiver of gov't aid.