With the reauthorization of the State Children's Health Insurance Program (SCHIP) under consideration in early 2009, an important question is the extent to which uninsured children could be covered under employer-sponsored insurance through premium assistance programs, which use public funding under Medicaid and SCHIP to subsidize employer-sponsored insurance (ESI). New data indicate that just 4.6 percent of all Medicaid-eligible uninsured children and 15.9 percent of all SCHIP-eligible uninsured children have a parent with ESI coverage, suggesting that premium assistance programs may not make a substantial dent in the uninsured problem facing children since, as a practical matter, they would target at most only an estimated 440,000 uninsured children who are eligible for public coverage. The fact that so few uninsured children have parents with ESI coverage highlights the importance of increasing take-up in Medicaid and SCHIP among eligible children. (Contains 2 figures and 34 notes.)