House Democrats, convinced that President Bush blundered by vetoing an expansion of a children's health care program, plan to approve a very similar bill this week even as the administration offered new concessions Tuesday.

The Democrats' revised bill would reduce the number of adults and higher-income families potentially eligible for the health insurance subsidies, presumably making it easier for Republicans to back it while saving face. But on the key issue of spending, Democrats say they will not budge from the original $35 billion pricetag.

Bush had recommended a spending increase of $5 billion over the next five years in the State Children's Health Insurance Program, enough to cover children in families generally with incomes at twice the federal poverty level — $41,300 for a family of four.

Health and Human Services Secretary Mike Leavitt said Tuesday that the administration is now willing to support, with conditions, covering children in families at up to three times the federal poverty level — $61,950.

Leavitt would not say specifically how much more money the administration would recommend for SCHIP, but he acknowledged that an additional $15 billion increase was "a rational number."

"We're willing to put substantially more money into covering the policy that we hear members of Congress advocate," Leavitt told the Associated Press.

House Majority Leader Steny Hoyer, D-Md., told reporters Tuesday that the Democrats' new bill would still expand the program from 6 million children now covered to 10 million. As for the proposed $35 billion increase, "you can't do the 10 million without that," he said.

Democrats would still pay for the expanded program with a 61-cent increase — to $1 — in the federal excise tax on a pack of cigarettes.

Leavitt said Bush would continue to oppose that or any other tax increase. He also said states should have to assure that low-income children are covered first, before eligibility is expanded to cover more middle-income families.

The administration's overtures would become moot if Democrats picked up just seven more House members who last week supported Bush's veto.

House Democratic leaders decided to hasten action on the bill Tuesday after dozens of colleagues told them the issue is extremely popular in their districts and should not be allowed to cool down.

"There's a big sentiment in our caucus to do it right away," said Rep. Jim Clyburn of South Carolina, the Democratic whip. Rep. David Price, D-N.C., said: "There's a sense that we have the high ground here, and we need to press ahead with it."

Republican negotiators, however, warned Hoyer that they may need several days to win over enough converts to the new bill.

Democrats said a revised bill could reach the House floor Thursday. Senate approval would come some time later, lawmakers said.

The children's health program is designed for families that make too much money to qualify for Medicaid, but not enough to buy medical insurance. The chief target is families earning twice the federal poverty rate or less. But some states cover families at three times the poverty level, and New York sought to go to four times the rate, reaching families earning nearly $83,000 a year.

The Bush administration rejected New York's request. But the president and his congressional allies repeatedly cited the $83,000 figure in arguing the proposed expansion was going too far.

Rep. Heather Wilson, R-N.M., one of the GOP negotiators who backed the vetoed bill and is trying to help craft a veto-proof revision, said she believed Democrats would agree to capping income eligibility at three times the poverty rate. Childless adults would be phased out of the program in one year under the proposed compromise, which is subject to change, she said.

The revised bill also would give states greater leeway to check the validity of applicants' Social Security numbers, she said, in a bid to counter criticisms that illegal immigrants might obtain health benefits.

But Wilson implored Democratic negotiators to slow down and "give people a chance to look at it."

Last Thursday the House voted 273-156 to override Bush's veto of the proposed $35 billion expansion. That was 13 short of the two-thirds majority needed. Forty-four Republicans joined 229 Democrats in voting to override.

Some Republicans who stood by Bush now feel the issue is hurting them politically, and they want a way out. They are the targets of Hoyer, Wilson and other negotiators hoping to make enough changes in the legislation to obtain a veto-proof House margin.

Some Democrats described the negotiators' proposed changes as little more than political fig leaves meant to give a dozen or so House Republicans enough cover to switch their votes. Once that happens, many House members feel, substantially more Republicans — and possibly Bush — will claim victory and embrace the bill.

Speaking of the proposed changes to the bill, Clyburn said Tuesday, "what may be minor to some may be major to others." He said the changes would be substantial.

The Senate, which passed the original bill by a veto-proof margin, is seen as likely to do so again if another House bill is approved.