(Adds White House comment in paragraphs 11-12.)

By Donna Smith

WASHINGTON, Oct 25 (Reuters) - The U.S. Congress and President George W. Bush headed for a fresh showdown over children's health care on Thursday after the House of Representatives approved a new bill expanding a popular insurance program despite a White House veto threat.

After failing last week to overturn the president's veto of the children's health insurance legislation, the House on Thursday passed a slightly reworked version of the measure that Bush has also vowed to veto.

The vote was 265-142, which is short of the two-thirds majority needed to overturn a presidential veto. The bill now goes to the Senate, which has a veto-proof majority in favor of the measure.

"This is a good day because we have another opportunity to extend to children -- 4 million of whom who are not covered by health insurance -- coverage," said House Majority Leader Steny Hoyer, a Maryland Democrat.

The new bill sought to allay Republican concerns that benefits would go to adults, high income families and illegal immigrants. But like the bill vetoed by Bush earlier this month, the latest version aims to provide coverage for as many as 10 million children, compared to the 6.6 million now enrolled.

Democratic leaders retained provisions that would boost spending for the program by $35 billion over five years above the current $25 billion five-year funding level. The extra money would be funded by raising taxes on cigarettes and other tobacco products.

The State Children's Health Insurance Program was created to help low-income and middle-income families who are unable to afford health insurance for their children, but who earn too much to qualify for Medicaid, the federal health insurance program for the poor.

With polls showing broad public support for expanding the program, Republicans opposed to the legislation have been put on the defensive as both parties jockey for position in next year's congressional and presidential elections.

The White House said the latest version, like the earlier bill, goes too far and does not address administration concerns in a meaningful way.

Administration officials have said Bush is willing to accept a $20 billion increase in spending and that raising tobacco taxes was unnecessary. During nearly seven years in office, Bush has voiced opposition to all tax increases.

"This bill does not address in a meaningful way the concerns the president raised, and so he will veto it if it reaches his desk," White House spokeswoman Dana Perino said in a statement.

"The bill still fails to ensure that poor children are covered first, it still allows states to cover adults, and it still raises taxes to move 2 million children from private health insurance to a government-run program," she said.

House Republican Leader John Boehner of Ohio said Republicans had the votes to uphold Bush.

While the earlier bill did not allow the program to cover illegal immigrants, the new version requires more rigorous background checks.

In addition, the bill states that despite claims to the contrary, coverage would not be offered to children of families with incomes over three times the federal poverty rate.

It also declares benefits to childless adults, now permitted in some states, will be phased out within a year.

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