Please do not take this answer as specific legal advise to your question, but only as general knowledge information to it. You should always consult a lawyer in more detail regarding yoru question.
A U.S. citizen, under the U.S. constitution, has a fundamental right to marry and have a family. The legal status of the foreigner the U.S. marries has no bearing in obtaining a license to marry. The license to marry is usually obtained at the clerk of court of the county where you reside. The expiration of the foreigner's visa to stay in the U.S. is something different which does not have anything to do with the marriage license, but with his or her legal status in the United States. He or she should attempt to legalize his/her status in the U.S. as soon as possible. One way could be through a Petition for Alien Relative once you marry. Please check further with an attorney regarding this procedure.
Alejandro R. Lopez, Esq.
Attorney only licensed to practice in Florida.