WASHINGTON — President Bush, in a confrontation with Congress, today vetoed a bipartisan bill that would have dramatically expanded children’s health insurance.

It was only the fourth veto of Mr. Bush’s presidency, and one that some Republicans feared could carry steep risks for their party in next year’s elections. The Senate approved the bill with enough votes to override the veto, but the margin in the House fell short of the required number.

The White House sought as little attention as possible, with the president wielding his veto behind closed doors without any fanfare or news coverage.

The State Children’s Health Insurance Program is a joint state-federal effort that subsidizes health coverage for 6.6 million people, mostly children, from families that earn too much to qualify for Medicaid but not enough to afford their own private coverage.

The Democrats who control Congress, with significant support from Republicans, passed the legislation to add $35 billion over five years to allow an additional 4 million children into the program. It would be funded by raising the federal cigarette tax by 61 cents to $1 per pack.

The president had promised to veto it, saying the Democratic bill was too costly, took the program too far from its original intent of helping the poor, and would entice people now covered in the private sector to switch to government coverage. He wants only a $5 billion increase in funding.

Mr. Bush argued that the congressional plan would be a move toward socialized medicine by expanding the program to higher-income families.

Democrats deny that, saying their goal is to cover more of the millions of uninsured children and noting that the bill provides financial incentives for states to cover their lowest-income children first. Of the over 43 million people nationwide who lack health insurance, 9%, or over 6 million, are under 18 years old.

Eighteen Republicans joined Democrats in the Senate, enough to override Mr. Bush’s veto. But this was not the case in the House, where despite sizable Republican support, supporters of the bill are about two dozen votes short of a successful override.

The House majority leader, Steny Hoyer, Democrat of Maryland, said Democrats were imploring 15 House Republicans to switch positions but had received no agreements so far.

Rep. Roy Blunt, Republican of Montana, said he was “absolutely confident” that the House would be able to sustain Bush’s expected veto.

Senator Lott, Republican of Mississippi, said Congress should be able to reach a compromise with Mr. Bush once he vetoes the bill. “We should not allow it to be expanded to higher and higher income levels, and to adults. This is about poor children,” he said. “But we can work it out.”

It took Mr. Bush six years to veto his first bill, when he blocked expanded federal research using embryonic stem cells last summer. In May, he vetoed a spending bill that would have required troop withdrawals from Iraq. In June, he vetoed another bill to ease restraints on federally funded stem cell research.

In the case of the health insurance program, the veto is a bit of a high-stakes gambit for Mr. Bush, pitting him against both the Democrats who have controlled both houses of Congress since January, but also many members of his own party and the public.

The Democratic Congressional Campaign Committee launched radio ads Monday attacking eight GOP House members who voted against the bill and face potentially tough re-election campaigns next year.

The president of the American Federation of State, County and Municipal Employees union, Gerald McEntee, said a coalition of liberal groups planned more than 200 events throughout the nation to highlight the issue.