He has a 6-month-old son who is a U.S. citizen.
Anibal Fuentes Aguilar is a day laborer who came to the U.S. from Guatemala when he was 16 years old.
Supporters say immigration officials are seeking to deport him after he was apprehended by border patrol. He had returned to Guatemala to attend his mother's funeral.
"What's to be gained by breaking up his family? Nothing can be gained," said Rev. Larry Greenfield, American Baptist Churches, Metro Chicago.
Immigration officials told Fuentes he can stay in the country another week or two while they consider his application to stop deportation.