WASHINGTON — House Democrats were unable today to override President Bush’s veto of their pre-election year effort to expand a popular government health insurance program to cover 10 million children.

The bill had bipartisan support but the 273-156 roll call was 13 votes short of the two-thirds that majority supporters needed to enact the bill into law over Mr. Bush’s objections. The bill had passed the Senate with a veto-proof margin.

The State Children’s Health Insurance Program now subsidizes health care insurance coverage for about 6 million children at a cost of about $5 billion a year. The vetoed bill would have added 4 million more children, most of them from low-income families, to the program at an added cost of $7 billion annually.

To pay for the increase, the bill would have raised the federal tax on cigarettes from 39 cents to $1.00 a pack.

“This is not about an issue. It’s about a value,” House Speaker Pelosi, Democrat of California, said just before the vote. “For the cost of less than 40 days in Iraq, we can provide SCHIP coverage for 10 million children for one year.”

Forty-four Republicans voted to override Mr. Bush’s veto — one fewer than GOP members who voted September 25 to pass the bill. Only two Democrats voted to sustain Mr. Bush’s veto compared with six who had voted against the bill. The two were Reps. Jim Marshall of Georgia and Gene Taylor of Mississippi.

“We won this round on SCHIP,” a White House spokeswoman, Dana Perino, said after the vote. She said a million-dollar lobbying campaign by several labor unions and advocacy groups to turn enough Republican votes for a successful override “didn’t work.”

Mr. Bush, anticipating that his veto would stand, has assigned three top advisers to try to negotiate a new deal with Congress. One of them, Health and Human Services Secretary Mike Leavitt said: “It’s now time for us to get to the hard work of finding a solution and get SCHIP reauthorized. We also have a larger task, to provide every American with the means of having an insurance policy.”

Republican opponents said the bill would encourage too many middle-income families to substitute government-subsidized insurance for their private insurance. The bill gives states financial incentives to cover families with incomes up to three times the federal poverty level — $61,950 for a family of four.

“That’s not low-income. That’s a majority of households in America,” Rep. Wally Herger, Republican of California, said.