More than two-thirds of senators are expected to vote for the bill when it reaches the floor later this week. Without a fresh infusion of federal cash, a dozen states are expected to run out of money for coverage of children next month.

Speaker Nancy Pelosi, Democrat of California, said supporters would keep fighting for the bill until they overcame the president’s resistance.

“This legislation will haunt him again and again and again,” Ms. Pelosi said. “It’s not going away, because the children are not going away.”

To help override the veto, Ms. Pelosi said: “We are hoping to galvanize support of the American people for this legislation. The president will find himself alone.”

Explaining his objections, Mr. Bush said, “The bill goes too far toward federalizing health care and turns a program meant to help low-income children into one that covers children in some households with incomes of up to $83,000 a year.”

Senator Charles E. Grassley, an Iowa Republican and a co-author of the bill, said the president’s charge was “factually incorrect.” The goal, Mr. Grassley said, is to sign up low-income youngsters who are already eligible but not enrolled in the State Children’s Health Insurance Program.

The White House insisted that, under the bill, it would be “next to impossible” for federal officials to deny a request from a state like New York, which recently adopted a law to increase its income limit to four times the poverty level, or $82,600 for a family of four.

Sponsors of the federal bill said it would cover nearly four million uninsured children, while continuing coverage for 6.6 million youngsters.

Among those lobbying for the program on Tuesday was Bonnie S. Frost of Baltimore. Her daughter, Gemma, now 9, has been in the program for eight years and received treatment for a traumatic brain injury after an auto accident in 2004.

The money provided in the bill is $35 billion more than the current level of spending and $30 billion more than Mr. Bush wanted.

To cover the cost, the bill relies on tobacco taxes, especially the cigarette tax, which would be increased to $1 a pack, from the current 39 cents.

The bill would make the following changes in the children’s insurance program:

• Dental services would have to be covered. Mental illnesses would generally be covered on a par with physical illnesses.
• States could cover pregnant women with low incomes. The federal government would reduce payments for coverage of parents and would gradually end coverage of non-pregnant childless adults in the program.
• Instead of directly providing coverage to children in low-income families, states would have new incentives to subsidize premiums for private health insurance offered by employers.