WASHINGTON (CNN) -- Three more Senate Democrats have signed onto a bill that would end most funding for the Iraq war next year. But even as support creeps forward, one key centrist Democrat has signaled he's unhappy with the idea.

New England Sens. Chris Dodd, D-Connecticut, John Kerry, D-Massachusetts, and Patrick Leahy, D-Vermont, are joining with Majority Leader Harry Reid, D-Nevada, in backing a bill written by war opponent Sen. Russ Feingold, D-Wisconsin. The measure would stop most funding for the Iraq war after March 31, 2008. It would provide money only for fighting Al-Qaeda, training Iraqis and protecting American government workers.

But there are more signs that Democrats have a steep climb if they want to pass the bill. On Tuesday, Sen. Ben Nelson, D-Nebraska, indicted he is against the general premise in the bill. His spokesman David DiMartino, issued a statement saying Sen. Nelson hasn't seen the Feingold/Reid proposal, but, "he does not support cutting funding for troops at war." Nelson is a centrist Democrat whose vote helped determined the fate of previous Iraq bills this year.

The funding cut idea is creating a stir in Washington, dropping into a tense standoff between the White House and Congress. The House and Senate are now working out the details of a critical bill that funds the war but sets a timeline to pull troops out of Iraq. The president has threatened to veto that measure. And in response, Democrats are using this second bill to tell the White House they're ready to take more aggressive action and end funding.

The back-and-forth timeline is important. President Bush has insisted the military needs more funding in coming weeks or commanders would have to cut back. But Reid told reporters in Nevada that the president is not being honest.

"The president's misleading the American people," he said. "The troops aren't about to run out of money."

A report by the Congressional Research Service concluded that troops in Iraq wouldn't be affected by funding issues until July.