Yes they are.
The well established number is that 50% of them are either illegals or the descendants of illegals.
There children are Americans at birth thru birthright citizenship. It is the current law of the land as much as you or I might disagree with it.
The U.S. Supreme Court has held that the U.S.-born children of permanent resident aliens are covered by the Citizenship Clause, but the Court has never decided whether the same rule applies to the children of aliens whose presence in the United States is temporary or illegal.
Some eminent scholars and jurists have concluded that it is within the power of Congress to define the scope of the Citizenship Clause through legislation and that birthright citizenship for the children of temporary visitors and illegal aliens could likely be abolished by statute without amending the Constitution.
