Washington ? Defying President Bush’s veto threat, a bipartisan group of lawmakers issued details Friday of a planned expansion of a children’s health insurance program.

The House plans to vote Tuesday on the measure, which would add $35 billion over five years to the program. It would be financed by raising the federal cigarette tax to $1 per pack, a 61-cent increase.

Bush has vowed to veto the measure, and lawmakers say it may be difficult to override his veto in the House – where a two-thirds majority is needed. The president says the bill is too costly, covers middle-income families that can afford insurance and involves an unacceptable tax increase.

Congressional Democrats overwhelmingly back the measure, but it also has drawn substantial Republican support.

“This legislation will get the Children’s Health Insurance Program back on track and reclaim precious resources for low-income kids,” Sen. Charles Grassley, R-Iowa, said in a statement. Sen. Orrin Hatch, R-Utah, urged Bush to accept what he called “a true compromise.”

The program expires Sept. 30. Assuming the House and Senate pass the bill next week and Bush promptly vetoes it, Congress probably would hastily approve an extension of the program under its current rules, lawmakers said.

The state-federal program is designed to provide health coverage to families whose income is too high to qualify for Medicaid, but not high enough to afford private coverage. More than 6 million people, primarily children, participate.

The proposed change would add about 4 million more.

The bill’s backers reject Bush’s claim that it would steer public money to families that can readily afford health insurance. The bill would provide financial incentives for states to cover their lowest-income children first, they said.

The bill would overturn the administration’s recent guidelines that would have made it difficult for states to steer CHIP funds to families with incomes exceeding 250 percent of the official poverty level. Under the legislation, states would have to show progress in signing up more low-income children before directing money to families with higher incomes.

The House passed a bill on Aug. 1 that would have increased CHIP funding by $47 billion over five years, and would have made several changes to Medicare. A Senate bill, passed the next day, omitted the Medicare changes and called for a smaller increase in funding.

White House press secretary Dana Perino said the bill “goes far beyond SCHIP’s mandate by covering some higher income households and adults.”

Bush opposes the approach because he says it takes the program away from its original intent of covering poor children, moves millions who now have private health insurance into government-run health care and is an incremental step toward a government-run health care system, she said.

“Once the Democrats finish their political posturing,” Perino said in a statement, “the president looks forward to working with Congress to pass SCHIP reauthorization legislation he can sign.”