The president has complained that the bill that emerged from Congress would steer the S-chip program away from its core purpose by expanding the program to cover some middle-class families, including some with annual incomes as high as $83,000, while failing to cover some deserving children.

“I want you to think about that,” Mr. Bush said. “If you’re making up to $83,000 in certain states, you’re eligible for the program, and yet half a million poor children aren’t being helped.”

The New York State Legislature this year passed a bill that would have covered children in families with incomes up to 400 percent of the poverty level, or $82,600 for a family of four. The Bush administration rejected New York’s proposal last month, arguing that it would have allowed the substitution of public coverage for private insurance.

And despite the president’s statement that “certain states” make children in families with $83,000 incomes eligible, New York is the only state that has expressed a desire to raise its income limit above $80,000. Mr. Bush has offered a plan to spend $5 billion more on S-chip over the next five years, versus the $35 billion in the next half-decade provided in the bill just approved by Congress. The bill that cleared Congress would add about four million children to the roughly six million already covered.

The issue has divided Republicans like few others, with several prominent lawmakers who are normally loyal to the White House opposing Mr. Bush on this issue. The bill was approved in the Senate by 67 to 29, with support from 18 Republicans  just enough to guarantee that a veto can be overridden.