Legal Question in Immigration Law in Georgia

Yes, there is a way to obtain a green card without having to go to Mexico. For example, if she came to USA on a visa and was inspected and admitted, and later her status had expired and she became "illegal". However, if she came to USA illegally and no one ever petitioned for her in the past, she will be required to go back to Mexico and apply for 1) visa and 2) extreme hardship waiver.

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When you say she is here illegally that doesn't give enough information to answer you, and you need to see a good immigration lawyer (that is not my specialty).

If she came illegally, she will likely have to go back and apply for a visa. If she overstayed a visa, she may have other remedies to stay.

It depends on how she entered the US and if any prior immigration petition was ever filed for her in the past.

You may find comprehensive information on the process here:

http://www.msclaw.com/Green_Card_for_Spouse.html