House Democrats are having a hard enough time rallying a deflated base as their domestic agenda flounders. But as they return to town this week, they are set to get a fresh reminder of a lingering issue that could depress their liberal flank even further: the debate over President Barack Obama’s proposed troop increase in Afghanistan.

Consideration of funding for the 30,000 additional troops is not expected to start in earnest until next month at the earliest. But the White House will get an early look at Congressional Democratic support for the buildup as soon as this week, when Rep. Dennis Kucinich (D-Ohio) offers a resolution calling for a swift end to the eight-year-old war.

Kucinich’s bid to end the conflict has no chance of passing, but it threatens to split the Democratic Caucus at a time when Members are struggling to unite and revive their stalled domestic agenda.

In the short term, the vote will give a forum to anti-war liberals eager to go on record opposing Obama’s Afghanistan strategy.

But as with every galvanizing debate in the Democratic Caucus, what sets hearts racing in one flank gives heartburn to the other. Moderate Democrats are twisting their hands over what they view as a needlessly divisive vote that will force them to publicly back engagement in a war that many of their most vocal — and deep-pocketed — liberal donors abhor but that a majority of their constituents strongly support. “People with weird liberal enclaves in their districts don’t need this vote,” one senior Democratic aide said.

Congressional Progressive Caucus Co-Chairwoman Lynn Woolsey (D-Calif.) doesn’t have much sympathy for anyone who would skip such a vote.

“I see this as a very positive and symbolic vote for those of us who want to end the war,” she said. “There are a lot of votes that many of us would like to avoid, but that’s why we got elected to Congress. It’s a very, very important vote, and it’s important that their constituents and America understand where they stand.”

A senior Democratic leadership aide said party leaders aren’t whipping the measure. “As on all matters related to war, Members will vote their conscience,” the aide said.

But another aide said top Democrats would at least make the case to their rank and file that it would be premature to withdraw now before military commanders have had a chance to see whether the strategy is working.

Another leadership aide downplayed the chance of the vote ripping apart the Caucus and said there remains a strong well of support for the president.

“I think people were generally supportive after the president’s speech, and we’re kind of keeping our powder dry waiting to see results,” the aide said. “Progress made in the last week in making some key captures helps shore up the president’s strategy.”

But the White House can’t rely on hands-on support from the top House Democrat when it presses lawmakers to fund the troop buildup through a supplemental spending bill in the coming weeks. Speaker Nancy Pelosi (D-Calif.) has made it clear that she will not whip her Members to support the package, as she did last spring.

“What I’ve told the Members is to give the president room, to listen to what he has to say,” she told reporters in December. “That we will provide the briefings and they will have the information, but I can’t — this for Members is a vote of conscience — war votes are votes of conscience and of their constituents.” Pelosi declined to say how or whether she would vote on the measure.

Obama has already proposed adding assorted other spending to his $33 billion supplemental including continued disaster relief for Hurricane Katrina and Midwest floods as well as billion-dollar settlements with black farmers and Indian trusts. The Pentagon wants the bill passed by spring to keep the war effort on track.

Woolsey said there will also be an effort to force withdrawal language onto the supplemental. “We control the purse strings,” she said. “That too will be a vote, on whether or not they will keep supporting sending our troops to Afghanistan.”

The war isn’t particularly popular with the public, but opposition within Congress has been relatively muted compared with the opposition to the war in Iraq that helped carry Democrats to power in 2006.

Nevertheless, a liberal Democratic strategist said the desire for a more clearly defined strategy and an exit plan is growing among House Members. “It is extremely difficult for them to justify the ongoing loss of life and staggering cost to our economy when it appears all we’re doing is propping up the corrupt Karzai regime,” the strategist said.

And high unemployment rates here at home aren’t making it any easier for Democrats to support the war, either. “I think that there’s the very real possibility that the American people will be ready to hear an argument that our national interest in Afghanistan can’t possibly be worth the staggering cost. Our economy is in tatters,” the strategist said.

Woolsey said she offered an amendment years ago to end the war in Iraq, and she credited that with helping build anti-war momentum. Kucinich’s resolution could do the same, she said.

Even so, Woolsey said the Progressive Caucus leadership does not plan to whip on the resolution one way or the other.

She also said many of her constituents remain confused about what to do in Afghanistan. They support Obama but are weary of the war.

“People want to give him the benefit of the doubt,” Woolsey said. “It’s not that I don’t want to give him the benefit of the doubt, I just don’t think we should be there in the first place.”