(Adds report on Republican lawmakers meeting with Bush)

By Richard Cowan

WASHINGTON, May 9 (Reuters) - Democrats in the U.S. House of Representatives said on Wednesday 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 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 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.

Defense Secretary Robert Gates told a Senate panel the two-step funding idea would create budget nightmares in the Pentagon. "The bill asks me to run the Department of Defense like a skiff and I'm trying to drive the biggest supertanker in the world," he said.

Cognizant of the opposition, House Democratic leaders appeared firm in their resolve to get the bill passed, which could give them a stronger negotiating position after the Senate passes a different measure, probably next week.

A bipartisan group of senators, many of them centrists, were meeting privately in an attempt to come up with a war-funding bill that could attract a solid majority of the 100-member Senate, according to Sen. Ben Nelson, a Nebraska Democrat.

'WE NEED HONESTY'

Nelson, who opposes setting deadlines now for withdrawing troops, would instead tie about $2.3 billion in reconstruction funds for Iraq to progress in stabilizing the country.

Meanwhile, Sen. Olympia Snowe, a Maine Republican, teamed up with Sen. Evan Bayh, an Indiana Democrat, in introducing legislation that could end U.S. combat in Iraq around April 2008 if Iraq fails to meet military and political goals for stabilizing the country.

Snowe returned this week from a visit to Iraq, where she said she found the "good news mixed, but the bad news deeply disturbing."

Republicans, nervous about the sinking popularity of the war and the Republican president, this week began talking about a September or October timeframe for seeing success in Iraq or demanding a new plan.

Eleven Republican congressmen met privately with Bush and his senior aides on Tuesday for what one described as an "unvarnished conversation" about the state of the Iraq war, NBC Nightly News reported on Wednesday.

The delegation, headed by Mark Kirk of Illinois and Charlie Dent of Pennsylvania, told Bush: "We need candor. We need honesty," and that the White House had lost its credibility on the war, NBC reported.

According to the report, Bush responded that he did not want to pass the war off to another president, particularly to a Democratic president, underscoring he understood how serious the situation was.

A White House spokesman said he would not comment on what Bush may or may not have said to lawmakers.

"He meets regularly with members of Congress and asks for their unvarnished opinions and frank advice. These conversations strengthen our relationship in our party, sharpen our policies and bring greater understanding on our positions, said spokesman Tony Fratto.

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