Illegal immigrants are just that illegal- they have no rights to health care, education, a job and/or anything short of swift deportation. If found here illegally rapid deportation should be followed by a ban from this country for a period up to 1 year per offense.
That being said, citizenship (when sought legally) should be easier to achieve rather than the current bureaucratic mess where it is easier to sneak across the boarder and get everything for free than be an honest person.