Supporters of a children’s health insurance bill are scrambling to salvage the measure, which had appeared doomed as soon as the House passed it last week.

The Senate might vote on the bill (HR 3963) as early as Tuesday. If it is unchanged from the version the House passed, its fate is sealed: President Bush will veto it, and the House will fail to muster the two-thirds majority required for an override.

But Sen. Charles E. Grassley of Iowa, the ranking Republican on the Finance Committee, is working with House Republicans as well as Finance Chairman Max Baucus, D-Mont., and Finance members Orrin G. Hatch, R-Utah, and John D. Rockefeller IV, D-W.Va., to draft an amendment to meet the demands of a group of House Republicans who say they might vote for the bill if changes are made to it.

“Sen. Grassley is hopeful that the ­Senate can make further changes that will enable legislation to become law, renewing and reforming this important program,” a spokeswoman said. If all sides, including House Democratic leaders, can agree to an amendment, it would be offered to the bill before the Senate passes it this week.

A bipartisan group of Senate and House aides met for about three hours Oct. 27 to discuss the bill and the range of issues complicating its passage, said Rep. Heather A. Wilson, R-N.M. And House Majority Leader Steny H. Hoyer, D-Md., met Monday with Republicans opposed to the bill to discuss changes, aides said.

“The debacle last week notwithstanding, I still think there’s the possibility of a broad, bipartisan consensus on a children’s health insurance bill,” Wilson said. “This should not be hard.”

A House Democratic aide said Hoyer’s meeting did not result in any agreement on changes that could be included in a Senate amendment.

The legislation would expand the State Children’s Health Insurance Program (SCHIP) by $35 billion over five years, to $60 billion. To pay for it, the bill would raise tobacco taxes, including a 61-cent increase in the cigarette tax, to $1 per pack.

The latest version is largely identical to an earlier bill (HR 976) that Bush vetoed Oct. 3, except for a few changes Democrats made in the hope of drawing more Republican support. The House fell 13 votes short of an override Oct. 18. The new bill passed the House, 265-142, on Oct. 25.

The most substantive change is a cap on eligibility for SCHIP at three times the federal poverty level, or about $62,000 for a family of four. The bill also would move childless adults out of SCHIP in one year instead of two.

The Democrats’ plan backfired, though, when Republicans complained that the revisions were not substantive enough and that the bill was rushed to the floor. Democrats forced a vote less than a day after introducing it, while some Republicans from Southern California were home helping constituents affected by wildfires. The timing further angered potential supporters.

“I think our members felt like [Democrats] couldn’t cancel the vote because they had already cut ads criticizing members for voting against it,” said Rep. Howard P. “Buck” McKeon, R-Calif.

The bill wound up losing the vote of one Republican who had supported the vetoed measure.

The day after the vote, a group of 36 Republicans sent a letter to Hoyer and Speaker Nancy Pelosi, D-Calif., outlining six changes they want in order to support the bill. Their top requests are that it include a mechanism that would require states to ensure that most children in families earning less than twice the poverty level are covered by SCHIP or Medicaid before expanding coverage to higher-income families; that it exclude all adults, including parents; and that it include stronger safeguards against illegal immigrants enrolling in SCHIP.

“Those three things could be worked out, I think,” said McKeon, who signed the letter.

But some Democrats, such as members of the Congressional Black Caucus, have warned their leaders they will not continue to support the bill if it is changed too much to satisfy GOP demands.

It was not clear Monday how long Grassley and other supporters would have to work on an amendment. Senate Majority Leader Harry Reid, D-Nev., filed for cloture Oct. 26 to limit debate on the bill, setting up a vote as soon as Tuesday. Democratic leaders have expressed frustration with Republicans, saying some of them express willingness to vote for the bill with revisions but then change their demands.

For example, two members who signed the letter to Hoyer and Pelosi said Monday that they have additional concerns about the bill that are not outlined in the letter.

Tom Price, R-Ga., said it would result in 53 percent of the nation’s children enrolled in Medicaid or SCHIP.

“I think it’s poor policy to expand government-run medicine to include over half the nation’s children in a government-run program,” Price said. The only way Democrats could satisfy that concern would be to reduce the cap on eligibility to less than three times the poverty level, which they say they will not do.

Virginia Foxx, R-N.C., who also signed the letter, said flatly she would not vote for a bill that allowed families earning up to three times poverty to enroll their children. “I think we need a bill that has [a limit of] 200 percent of poverty,” she said.

McKeon expressed more flexibility. “I understand you don’t get everything you want in legislation,” he said. “I also understand that 300 percent of poverty is different in Arkansas and New York and California.”

His concern, he said, is that by avoiding substantive talks with House GOP leaders, with Bush or with Republicans who would support it after further changes, Democrats are not negotiating in good faith. “I don’t need to be there, but I want someone in there who agrees with my position — the secretary [of Health and Human Services], a member of my leadership,” he said.

Wilson said she thinks Democrats and Grassley might be on the right track. “They’re negotiating with the right people, finally,” she said.