Democrats cited several reasons for their second thoughts about the wisdom of another vote on the child health bill. The cost of the bill has increased, according to the Congressional Budget Office, though the revenues expected from higher tobacco taxes are about the same. Under current rules, Congress would need to find a way to defray the extra cost.

In addition, time is short, and the Congressional calendar is packed with other issues.

Bruce Lesley, president of First Focus, a bipartisan advocacy group for children, said: “We definitely would prefer for Congress to vote on the legislation next year rather than this year. Why would you pass a bill now when, in six months, you could get a better bill covering more uninsured children?”

Since it was created with bipartisan support in 1997, the program has reduced significantly the number of low-income children who are uninsured.

The Census Bureau reported last month that the number of people under 18 without health insurance had decreased, to 8.1 million in 2007, from 8.7 million in the prior year. Economists say the number could climb this year because of the weak economy and rising unemployment.

The Congressional Budget Office estimates that the bill, financed by an increase in tobacco taxes, would reduce the number of uninsured children by 4.4 million by 2013. But at the same time, the budget office says, the bill could encourage some families to substitute public for private coverage, reducing by 2.3 million the number of children who would otherwise have private coverage.

A few House Republicans in tight races might switch sides and vote for the bill, in an effort to win the approbation of voters, Democrats say. But supporters of the bill believe that they would still not have enough votes to override a veto by Mr. Bush.

Hispanic, black and Asian-American members of Congress have complained that the bill does not provide coverage for legal immigrants who are now generally barred from benefits under Medicaid and the children’s health program during their first five years in the United States.

Many Democrats would like to lift those restrictions. But if they tried to do so, they could draw Congress into a bitter debate over immigration policy.