WASHINGTON, July 22 — After a rare bipartisan agreement in the Senate to expand insurance coverage for low-income children, House Democrats have drafted an even broader plan that also calls for major changes in Medicare and promises to intensify the battle with the White House over health care.

President Bush has threatened to veto what he sees as a huge expansion of the children’s health care program, which he describes as a step “down the path to government-run health care for every American.” The House measure calls for changes that the administration will probably find even more distasteful, including cuts in Medicare payments to private health plans.

Like the bill approved last week 17 to 4 in the Senate Finance Committee, the House bill would increase tobacco taxes to help finance expansion of the Children’s Health Insurance Program.

House Democrats hope to portray the issue as a fight pitting the interests of children and older Americans against tobacco and insurance companies. The White House says the Democratic proposals would distort the original intent of the children’s program, cause a big increase in federal spending and adversely affect older Americans who are happy with the extra benefits they receive from private health plans.

By packaging Medicare with the children’s health program, Democrats say, they have built a strong intergenerational coalition that could help them overcome a presidential veto. The House bill has already drawn support from two powerful groups, AARP and the American Medical Association, in part because it would prevent cuts in Medicare payments to doctors. But the House bill is likely to meet fierce resistance from some Republicans because it is more costly than the Senate bill and could undermine private Medicare health plans, which have been championed by Republicans for a decade.

The proposal comes as health care has risen to the top of the domestic agenda. Presidential candidates from both parties are searching for ways to overhaul the health care system, control costs and address the needs of the uninsured.

Lawmakers say they see an urgent need for action. The Children’s Health Insurance Program is set to expire on Sept. 30, and Medicare payments to doctors will be cut by 10 percent on Jan. 1 if Congress does not act.

On Sunday, House Democrats said that they would unveil their bill in the next few days and that they expected to push it through the House next week, before Congress leaves town for a monthlong summer recess.

Under the bipartisan Senate plan, the federal government would increase spending on children’s coverage by $35 billion over the next five years, for a total of $60 billion. House Democrats want to increase spending by $50 billion, which is 10 times the increase sought by Mr. Bush.

Representative Charles B. Rangel, the New York Democrat who is chairman of the Ways and Means Committee, said the House bill would “reverse the Republican drive to privatize Medicare,” by reducing payments to private health plans that care for 8 million of the 43 million Medicare beneficiaries.

Proponents of the private plans, offered by companies like UnitedHealth and Humana, say they provide more benefits than traditional Medicare.

But the nonpartisan Congressional Budget Office said the government paid the private plans, on average, 12 percent more than it would have cost to care for the same people in traditional Medicare. Moreover, it said, payments to the fastest-growing type of plan, known as private fee-for-service plans, are 19 percent higher than the cost of traditional Medicare.

The House bill would gradually reduce these payments so that Medicare would pay the same amount, regardless of whether a beneficiary was in a private plan or in traditional Medicare.

AARP, which represents nearly 39 million older Americans, and the American Medical Association said they would begin running television advertisements on Monday to secure passage of the House bill.

The bill, known as the Children’s Health and Medicare Protection Act, would block impending cuts in Medicare payments to doctors, giving them a modest increase in fees in each of the next two years while Congress tries to devise a new payment policy.

Under existing law, according to the latest annual report of the Medicare trustees, Medicare payments to doctors would be cut by 10 percent in 2008 and about 5 percent in each of the next eight years, for a cumulative reduction of more than 40 percent by 2016.

In the Senate Finance Committee, 6 Republicans joined 11 Democrats in defying Mr. Bush’s veto threat. The House bill was developed entirely by Democrats, who hope to win support from some moderate Republicans.

Cigarette makers are fighting the proposed increase in tobacco taxes, while insurers are lobbying against cuts in their Medicare payments.

“Cuts of this size would mean the end of a lifeline for many seniors,” said Karen M. Ignagni, president of America’s Health Insurance Plans, a trade association.

Michael J. Tuffin, executive vice president of the association, described the insurance industry’s “grass-roots strategy” to oppose the cuts in a recent e-mail message to member companies. Mr. Tuffin said “field operatives will organize small gatherings of seniors across the country” and rent minivans to take them to the district offices of House members, to “speak out against the cuts.”

Senator Jon Kyl, Republican of Arizona, said last week that the cost of the Democratic proposals was unsustainable. “We are making promises we can’t keep,” Mr. Kyl said.

In addition to expanding health care for children and curbing payments to private insurers, the House bill includes these provisions, as described in a written summary of the legislation and interviews with lawmakers:

¶ It would be easier for low-income Medicare beneficiaries to get additional help. Congress would simplify application procedures and relax the strict limits on assets, which now disqualify many retirees with modest savings.

¶ The secretary of health and human services would be allowed to expand Medicare coverage of preventive services like certain disease-detection screenings. To encourage use of these benefits, Congress would eliminate most co-payments and other charges.

¶ Medicare would pay primary care doctors, including internists and family physicians, to coordinate the care of some people in traditional Medicare. Researchers say such coordination improves care and saves money, especially for people with chronic diseases who may be seeing six or eight doctors.

¶ State insurance commissioners would be given more power to regulate marketing by agents and brokers selling private health plans to Medicare beneficiaries. State officials and consumer advocates say that some people have been tricked into enrolling in such plans by agents who use deceptive sales tactics.

¶ Congress would abolish a provision of the 2003 Medicare law that requires the president to propose changes in Medicare to limit its reliance on general revenue. Democrats fear that this requirement will be used to justify cuts in benefits or in payments to doctors or other health care providers.

In addition, the House bill would prohibit private Medicare plans from charging higher co-payments than traditional Medicare.

On Sunday, the National Governors Association, at its annual meeting, in Traverse City, Mich., declared that “urgent action is needed” to bolster the children’s health program. “Defaulting to a series of temporary extensions of the program would be untenable for states and the millions of children who rely on the program,” the governors said in letters to President Bush and Congress.