President Bush on Wednesday made good on his promise to veto a bill that would have expanded government health insurance for children, but then said he was open to compromising with Congress by spending more money on the program than his budget has proposed.

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Kevin Lamarque/Reuters
President Bush, speaking in Pennsylvania Dutch Country Wednesday, explaining his veto of a children’s health insurance bill.
“I do want Republicans and Democrats to come together to support a bill that focuses on the poor children,” Mr. Bush told a group of business people at a town-hall-style meeting here in Pennsylvania Dutch Country.

He added, “And if they need a little more money to help us meet the objective of getting help for poorer children, I’m more than willing to sit down with the leaders and find a way to do so.”

But Mr. Bush did not make a specific offer, and his plan, to spend $5 billion more on the program over the next five years, falls far short of the $35 billion expansion that passed with bipartisan support in Congress.

On Capitol Hill, Democrats and their Republican allies seemed in no mood to compromise; they vowed to overturn the veto before entertaining any deal.

“We’ve got to do what we can to try to override,” said Senator Charles E. Grassley of Iowa, the senior Republican on the Finance Committee, who was the bill’s lead Republican sponsor and had personally appealed to the president not to veto the measure.

There are enough votes to override the veto in the Senate, but not in the House. In a somewhat unusual move, House Democrats on Wednesday forced a vote to postpone the override attempt until Oct. 18, giving themselves two weeks to round up the roughly 20 votes they need. Mr. Grassley said he intended to personally appeal to House members who could provide the necessary votes to circumvent the president, and Democrats said they had already picked up a few.

The veto, only the fourth of Mr. Bush’s presidency, is a politically difficult one for the president, and he issued it in private Wednesday morning, without the fanfare and White House ceremonies he has employed when rejecting embryonic stem cell legislation and an emergency war spending bill that set a deadline for troop withdrawal from Iraq.

He then traveled here to make his case for the veto directly to the American people, via a nationally televised chat with a friendly audience made up of members of a local Chamber of Commerce group.

The topics included the war in Iraq, climate change, education, Iran’s nuclear program and subsidies for farmers. In an unusual departure for a White House that likes to keep its events under tight control, a woman wearing a T-shirt that read, “George Bush, your war killed my friend’s son,” was allowed to remain at the event, and the first question came from a war opponent, who said he wanted to ask Mr. Bush “man to man, taxpayer to president,” whether it was time to bring the troops home.

But the White House had another agenda: to explain Mr. Bush’s decision to reject the expansion of the health insurance plan — known as Schip, for State Children’s Health Insurance Program — which would have added four million children to the six million already covered.

Mr. Bush argues that the expansion is too costly and would push people who could afford private insurance onto the government rolls, steering the program away from its initial aim of helping poor children. He said that states like New Jersey, Michigan, Minnesota, Rhode Island, Illinois and New Mexico spend more money on adults than children, and he reiterated his contention, which the authors of the bill dispute, that the measure could benefit some families earning up to $83,000 a year.

“That doesn’t sound poor to me,” the president said.