President Barack Obama’s choice of Gen. David Petraeus to take over command in Afghanistan from Gen. Stanley McChrystal received near-universal praise on Capitol Hill but did nothing to change the deepening fault lines over America’s longest war.

If anything, Obama’s decision to relieve McChrystal following his flip criticism of senior administration officials in a Rolling Stone interview stirred up what has been a simmering debate over the mixed results to date of the costly surge and counterinsurgency strategy ordered by Obama last year. Anti-war Democrats called on Obama to rethink his war plan in advance of a key vote on a supplemental war spending bill in the House.

But Sens. Lindsey Graham (R-S.C.), John McCain (R-Ariz.) and Joe Lieberman (ID-Conn.) warned Wednesday that Obama’s Afghanistan war policy could be jeopardized by his insistence on starting to withdraw troops next year.

They offered Obama high praise for his decision to replace McChrystal with Petraeus. However, they said that decision alone does not solve other issues undermining the war effort, including White House disunity over the president’s Afghanistan policy and the poor relationship that key diplomatic officials have with the top military brass leading combat operations.

“We are confident that Gen. Petraeus’ leadership will have a very positive effect on the situation in the region,” said McCain, the ranking member on the Armed Services Committee. “But we still have concerns about the civilian side.” McCain suggested that Obama consider sending former Iraq Ambassador Ryan Crocker to join Petraeus in Afghanistan.

Graham was more critical in his appraisal of where the war effort stands. He said the Obama administration’s attaching a date for withdrawal of troops — regardless of the conditions on the ground — would have severe, adverse effects on the prospects for victory.

“Dave Petraeus is our best hope. If things don’t change, nobody can pull it out in Afghanistan. We’re not doing as well as I would like; there’s uneven progress. The civilian side, in my view, is completely dysfunctional,” Graham said. “If we don’t change quickly, we’re going to lose a war we can’t afford to lose.”

“The July 2011 [withdrawal date] policy is confusing,” Graham continued. “It undercuts the war effort; it empowers our enemies, it confuses our friends, and I think it needs to be re-evaluated.”

Petraeus, meanwhile, received plaudits from leaders across the spectrum, and his Senate confirmation is expected early next week after an Armed Services Committee confirmation hearing.

“I don’t know if we could have found anyone better,” Minority Whip Jon Kyl (R-Ariz.) said.

House Armed Services Chairman Ike Skelton (D-Mo.) also gave Obama’s choice a thumbs-up.

“Gen. Petraeus is the best that we have,” he said. “It is time to move on and return our focus to waging the war in Afghanistan.”

But while the Petraeus brand has a special sway over Members of both parties, anti-war lawmakers say the president should rethink his strategy, not just who is running it.

“This was an opportunity I think a lot of use were hoping for to step back and re-evaluate things,” Rep. Patrick Kennedy said. “It’s a chance to take a deep breath and take a look at the overall picture here.”

The Rhode Island Democrat said he still supports Petraeus and holds out hope that he could be convinced to change course. “He’d be the most credible person, in fact,” Kennedy said. “He could be our biggest ally.”

But Rep. Dennis Kucinich said the president missed a chance to pull out of a war gone bad. “It’s a new general but the same old failed counterinsurgency strategy,” the Ohio Democrat said. “We’ve got to get out.”

“Is it starting to sound like Vietnam to anybody here?” Rep. Peter DeFazio asked on the House floor, pointing to corruption, costs and other problems. “This echoes that failure.”

The Oregon Democrat urged Obama to reconsider his statement that he wasn’t changing policy and to consider a much less expensive strategy focusing on terrorism.

That had at least some support across the aisle.

Rep. Jeff Flake said Obama should shift to a more limited counterterrorism strategy. The Arizona Republican said the current strategy hasn’t worked very well, and he pointed to concerns that the massive U.S. footprint in Afghanistan is actually leading to the funding of warlords and the Taliban to truck goods from base to base.

“We’re not only tolerating a parallel authority structure outside of government, we’re … funding it,” Flake said.

“I have enormous confidence in Gen. Petraeus, but even the most competent commander can only implement a mismatched strategy with limited results,” he said.

John Stanton contributed to this report.