Is A Child Born On U.S. Soil considered an illegal immigrant even though the parents are?

Except in limited circumstances a child born on United States soil is a United States citizen. The child's parents' immigration has no bearing on his/her citizenship. You can read more about citizenship at http://myattorneyusa.com/the-citizenship-clause-and-jus-soli-citizenship-citizenship-by-birth-in-the-united-states.