By Richard Cowan

WASHINGTON (Reuters) - Democrats in the U.S. House of Representatives on Wednesday said they would press ahead with a new Iraq funding bill, despite a White House veto threat and a cold Senate reaction to a bill that would dole out combat funds in pieces and force a July vote on withdrawing troops.

"The House bill is going to change," promised Senate Majority Leader Harry Reid, a Nevada Democrat.

White House spokesman Tony Snow told reporters President George W. Bush would veto the House bill if it reached his desk.

While House Democratic leaders want to pass the new war funds bill by late Thursday, support was being measured and some aides said the vote could slip to Friday or next week.

Under the bill, which is not expected to become law, Bush would get a $42.8 billion down payment. Then, after getting White House war progress reports in July, Congress would cast votes late that month on whether to release an additional $52.8 billion to continue fighting in Iraq through September, or whether to use the money to withdraw most of the troops by the end of this year.

Bush wants all the money for fighting the war now and without conditions.

Defence Secretary Robert Gates told a Senate panel that the two-step funding idea would create budget nightmares in the Pentagon.

"The bill asks me to run the Department of Defence like a skiff and I'm trying to drive the biggest supertanker in the world," he said.