What can I do when a TA asks me to marry her so that she can obtain a green card? This pertains to an American university graduate program.

A TA recently surprised me with a proposition to marry her (we've neither dated nor hooked up), so that she could obtain a green card to stay in the United States -- she wants to leave the STEM fields and go into the creative / artsy stuff (eg, dreams of having a creative career in Los Angeles), which means she likely won't earn a work visa to stay in the US.  

She essentially offered a blank check from her family, so long as the amount is less than the investment green card amount of 500k dollars (something that I did not know even existed).

My question is: putting aside legal, personal and ethical questions, what are the academic implications of this situation? At what point could I get into trouble with the university; from having such discussions with her or later, if I actually did something?  Could I be dismissed from the university or have my degree revoked later on?  What about implications regarding any funding that I might have from the university or from the government (eg, grants, loans)?

Edit:  Thanks to those offering marriage strategies and interpretations of the law, but I had hoped to stay on-topic and focus on the academic implications.  Currently, I am reduced to voting for an on-topic answer that I have some qualms about, since, as mentioned in Dan Romik's comments, the answerer focuses on reporting harassment, when I have not been harassed at all.  Perhaps the community can vote to reopen the question to allow for more, on-topic answers.
I am a U.S. citizen and happen to have a foreign spouse, so I've had some personal experience with this.

It could conceivably work if the two of you had known each other intimately for some time, even if you had a George Bernard Shaw, separate bedrooms kind of relationship.  But if you are just acquaintances, it is unlikely the two of you would get through the interview process successfully.  In separate interviews, you would be asked an unpredictable set of questions about your shared personal history.  There are sample interview questions posted online, e.g. https://www.usavisanow.com/marriage-green-card/marriage-green-card-faq/marriage-green-card-interview/ and http://www.alllaw.com/articles/nolo/us-immigration/what-happens-green-card-marriage-interview.html.

In addition, USCIS (formerly INS) would need to see documentation that your finances have been shared and inextricably intertwined for some time.

You could enjoy the fantasy together for an evening, with the Dépardieu film Green Card.



P.S. I have heard about a businessman's visa, which her budget might be enough for, but I don't know much about it.