My girlfriend has overstayed her visa and wants to marry to obtain a green card. I'm only willing to do it if there is an air tight prenuptial agreement. Will she still obtain a green card if this happens?
Whether or not a green card is issued is not really the relevant question, the question is whether it is legal. Many people engage in sham marriages, and then are prosecuted for it. 8 USC 1325 says that
Any individual who knowingly enters into a marriage for the purpose of evading any provision of the immigration laws shall be imprisoned for not more than 5 years, or fined not more than $250,000, or both.
Prosecution under other provisions such as 18 USC 1001 have also resulted.
In addition to the element of entering into a marriage to avoid immigration law, sham marriage prosecutions have included the elements of payments for the deception, plus the fact of not living together as man and wife. I have not found evidence of any prosecution for marriage fraud based solely on the intent to avoid immigration law (i.e. no payment and the couple did live together as husband and wife). But, the statute does not say that payment is a prerequisite for prosecution, nor does it say that living together overcomes the stated prohibition of the law.
Your lawyer should advise you how to proceed in this situation. If you add the elements of payment and not living together, the conclusion that this is fraudulent marriage is strong and probably provable by the government. If this is just a secret between the two of you (and your attorney), and you maintain a viable marriage for the requisite 2 years, there may not be a basis for prosecution under 8 USC 1325, since there may not be sufficient proof of true intent. The content of the prenup could be irrelevant, or could support a fraudulent-intent prosecution, depending on what it says.
There's nothing in the law explicitly forbidding someone with a prenuptial agreement from sponsoring his or her spouse, but I suppose it could influence the assessment of whether the marriage is genuine. The preparation of the prenuptial agreement should involve an immigration lawyer, who should be able to advise as to the effects of any given provision in the agreement.