President Bush's health secretary expressed hope Sunday for a deal with the Democratic-run Congress on expanding children's health insurance even as the House speaker worked to round up enough Republicans to override a veto.

"Everybody wants children to have health insurance," Health and Human Services Secretary Mike Leavitt said. "The president has already said, 'I want a compromise."'

Leavitt added, "If it takes more money, we'll put it up." He did not cite a figure.

Bush vetoed legislation last week that would increase spending for the State Children's Health Insurance Program by $35 billion over five years. Bush has called for a $5 billion increase.

Several Republicans in both the House and Senate have sided with majority Democrats on the issue, and the Senate has enough votes to override the veto. But in the House, Speaker Nancy Pelosi has delayed an override attempt until Oct. 18, saying she needs to attract support from 14 more Republicans.

"It's hard to imagine how we could diminish the number of children who are covered," said Pelosi, D-Calif., in an interview broadcast Sunday. "The president calls himself 'the decider,' and I don't know why he would want to decide that one child has health care and another does not."

"So we take it one step at a time. And right now, we have the next 10 days to two weeks to try to peel off about 14 votes in the House," she said.

The program provides health insurance to children in families with incomes too great for Medicaid eligibility but not enough to afford private insurance.

Bush and Leavitt have decried the spending increase primarily supported by Democrats as unnecessarily subsidizing middle-income people as part of Democrats' "goal of government-run health care for every American."

Leavitt appeared on ABC's "This Week," Pelosi was interviewed Friday by "Fox News Sunday."