This is an issue that Michelle Malkin has raised and I have posted on here and here.
The cost to cover these folks are estimated to be about $30 billion but The Center suspects it may actually come in as less because many of those illegals would not enroll. If Obama gets an amnesty program through and they become legal, then the costs go back up.
The Corner at NRO points out that programs that use a verify system reported falling caseloads whereas those that didn't reported increasing caseloads:
Not conclusive, true, but it is an indication of how ObamaCare will go if immigration status isn't screened.
We already have precedent for avoiding the illegal issue. When Federal ID requirements went in for Medicaid in 2006, Medicaid caseloads immediately started falling. It isn’t conclusive but it sure is suggestive.
SCHIP caseloads immediately started rising, at least in my state. SCHIP does not require ID. In my state it provides many of the same benefits as Medicaid and costs just $35 a year, max.