I do not know South Carolina law specifically but I have not heard of a state making it illegal to marry an undocumented alien. The next question is what immigration options he may have to regularize his status and we would need to ask him a lot of questions to determine this.
You would need to check the specific marriage requirements in South Carolina. However, in general most states do not prohibit undocumented aliens from marrying. As to whether your fiancee could seek immigration status after you marry more information is needed including his manner of entry, immigration history, criminal history, etc. President Obama has passed no new laws; the President only has the power to sign into law legislation passed by Congress. President Obama has created a program that allows certain qualifying individuals to remain in the United States and obtain employment authorization, but this program confers no legal status. I would encourage you and your fiancee to schedule a consultation with an experienced immigration attorney.
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Check South Carolina requirements for issuance of marriage certificates. Most states require a state-issued valid picture ID, or alternative proof that the person appearing at the marriage is who they say they are.
This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.