WASHINGTON — In a deepening conflict with the White House, Democrats pushed a revised children’s health bill through the House yesterday but lacked the votes to overcome a threatened second straight veto by President Bush.

The vote was 265–142 on a bill so politically charged that one Republican bluntly accused Democrats of timing the events to dovetail with attack ads planned by organizations supporting the legislation.

“They won’t take yes for an answer,” Rep. Rahm Emanuel of Illinois said, as Democrats vehemently denied the charge. He said the legislation included changes demanded by GOP critics of the earlier vetoed bill, including one to prevent illegal immigrants from gaining benefits.

The measure now goes to the Senate.

Rep. Steny Hoyer, a Democrat of Maryland and the majority leader, told reporters additional changes are possible before it heads to the White House. At the same time, he added, “I don’t want to be strung along” by Republicans merely feigning an interest in bipartisan compromise.

The legislation is designed chiefly to provide coverage for children whose families make too much money to qualify for Medicaid but not enough to purchase private insurance.

In general, supporters said it would extend coverage to children of families making up to 300% of the federal poverty level, or about $62,000 for a family of four.

At that level, congressional officials said, it would cover about 4 million children who now go without, raising the total for the program overall to 10 million kids. The $35 billion cost over five years would be covered by an increase in the tobacco tax of 61 cents a pack. The vote unfolded one week after the House failed to override Mr. Bush’s earlier veto, and indicated that the changes Democrats had made failed to attract much, if any, additional support.