We seem to have a Bush endorced stealth campaign to allow them to remain here: LINK
And their numbers roughly equal the number of Americans unemployed and undoubtedly will require government assistance to pay their way.
If the illegals weren't here, there would be jobs that employers would have to compete to fill at market wages.. Retaining employees may require benefits as an incentive, as opposed to handouts from the government it would be a tool employers use to get and keep help.