The CRS statement posted in this thread is not a CRS statement, it is a press statement by FAIR, an anti-immigration group.
The section of the House bill quoted here applies to any federal monies to illegal aliens, it does not apply to only one section.
Your comment about the exchange displays a lack of knowledge about what the exchange will be - a marketplace to purchase insurance. An illegal alien is not barred from purchasing insurance in the health insurance exchange created under the bill, but they would could not purchase it with federal money. They are not eligible, under any of the bills in the House or Senate, from receiving federal money. The actual CRS statement says that. The FAIR statement does not.
Long and short, you are getting spun. There is NO money for illegal aliens under any of the bills.
The actual CRS statement - with no anti-immigrant spin:
bad link ...edited out
edit: gah, that is not the link, either. have to google it.