He will not be deported fro marrying a US citizen. However, depending on his immigration and other background history, he may be eligible to obtain permanent residence (green card). You should consult an experienced immigration lawyer for that matter.
It depends on whether he has a criminal record or is just an overstay and what you status is (U.S. citizen, Permanent Resident, etc.) If you are a U.S. citizen you can petition him immediately after you get married. However, he will probably have to return to his home country for a period of time and go through consular processing.
If you get married, your marriage will not cause his deportation. Most likely, you will not be able to "fix his papers" now; but the law is expected to change. And, even under the present law, if he gets arrested by the Immigration, his being married to a U.S. citizen or permanent resident might give him a chance to fight the deportation.
If you are a citizen you may petition for him once married. Whether he can stay depends on his manner of entry, length of stay in US, and criminal history if any. I suggest consulting with an attorney so you can discuss in detail.
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