WASHINGTON, Oct. 9 — There have been moments when the fight between Congressional Democrats and President Bush over the State Children’s Health Insurance Program seemed to devolve into a shouting match about who loves children more.

So when Democrats enlisted 12-year-old Graeme Frost, who along with a younger sister relied on the program for treatment of severe brain injuries suffered in a car crash, to give the response to Mr. Bush’s weekly radio address on Sept. 29, Republican opponents quickly accused them of exploiting the boy to score political points.

Then, they wasted little time in going after him to score their own.

In recent days, Graeme and his family have been attacked by conservative bloggers and other critics of the Democrats’ plan to expand the insurance program, known as S-chip. They scrutinized the family’s income and assets — even alleged the counters in their kitchen to be granite — and declared that the Frosts did not seem needy enough for government benefits.

But what on the surface appears to be yet another partisan feud, all the nastier because a child is at the center of it, actually cuts to the most substantive debate around S-chip. Democrats say it is crucially needed to help the working poor — Medicaid already helps the impoverished — but many Republicans say it now helps too many people with the means to help themselves.