How Are US Citizenship Applications Affected by Marriages to an Illegal?
If INS feels you are seeking US citizenship in so that your illegal wife (no green card) can stay legally, they may ask you to go to a fraud interview in order to prove your marriage is valid and not just to get her a green card. They may ask to speak with her and interview her. They could deport her. They could tell you to file a I-601 form (Hardship) or I-130 to adjust the illegal status to legal. She may have to wait up to 10 years, once deported, before she applies to enter legally.
If the alien is illegal because he or she snuck into the United States without any visa or permit, than that person cannot "adjust status" and has to leave the country before obtaining a green card. If the person was illegally in the country for more than a year, than he or she is barred from ever coming back for 10 years (known as the "10-year-bar") The only way to overcome having the 10-year-bar is by the US citizen spouse filing a petition for a waiver of the bar. The petition has to prove that it would cause extreme and exceptional hardship to him or her to move to his or her spouse's country.
Once you are married you can start the process by filing the I-130. once it is approved, he\she will have to go back to Mexico for an interview to get his visa at the American consulate in Mexico. He\she will be denied the visa because he was illegaly present in the US for over a year. At that time, he will be instructed to file the I-601. You will have to present evidence proving that you could not live in Mexico. This would include evidence of medical problems you may have, financial obligations in the US, familial obligations (i.e. caring for aging parents or disabled relatives.) and anything else that would make it impossible for you to move to Mexico. You have to prove that the hardship would be ABOVE and BEYOND the hardship that could be obviously expected. Not easy to do.
The Green Card holder would need to file an immigrant visa petition after marriage under the F2a family preference category. However,those petitions take 5 years before they are valid for use. Until that time, they provide no immigration benefits at all. Plus, it will be impossible for the illegal immigrant to adjust to green card status while in the US. He'd have to go home for an immigrant visa interview than then apply for a waiver.
The person here legally, the Green Card holder, may have the whole process to become a US citizen delayed or stopped. On the other hand, INS may conclude nothing else occurs to the permanent resident who is applying for US Citizenship and the deportation of the illegal wife is hardship enough.