Helping the uninsured children of America

Of the 6.6 million uninsured American children in 2009 (7.2% of all children), about 2/3 were actually already eligible for health coverage through Medicaid or CHIP. About 40% of that 7.2% were children of illegal immigrants, but are American citizens by birth. Now with Obamacare, things will really be screwed up, and it's possible if CHIP funding lapses (which logically shouldn't be needed if we've got this other wonderful plan), there could be more uninsured children than before the ACA.

Now, I'm no math genius, but if 92.8% of all American children were insured either by private insurance or their parents' employer, and 40% of the uninsured were children of illegal immigrants, and 2/3 were eligible for a government plan already in place, were there no geniuses in this administration would could figure out a way to help these children without messing up every other child's plan?

Statistics from JAMA, May 7, 2014.