What happens if I marry an illegal alien?

I got my girlfriend pregnant more than a year ago. I found out shortly after that she was an illegal alien. She came to this country (USA) legally on a tourist visa, but overstayed by several years and has since been working in the US even though it is illegal for her to do so( which is where we met). We now have a daughter and are considering wether to get married or to go our seperate ways, which for her means returning to Mexico. My question is, if we did get married, what would the process be to make her a legal citizen, and if that isn't possible, what are the repurcusions of marrying an illegal alien?