Razor Fish

My girlfriend, a German National, was turned back in Atlanta en route
from Frankfurt to LA, where she has been staying. The reason: she has
over stayed her visa by four months, give or take a week or so. Now
she wishes to reenter the US but with a valid visa, preferably a work
visa sponsored by a US corporation.

Her circumstances are rather complicated, I think, in that she has had,
in the past, both a student visa and a work visa. Both expired. While
here she has been not particularly responsible financially (has
defaulted on more than one credit card, the way I understand it).

The question is: is there any point in applying for a work visa for her
and how in depth does the INS go in the discovery process in the
pendancy of an immigration filing? Is marriage a better route? This
group's esteemed opinion would be greatly beneficial.

Thank you,

George