Sen. Joe Lieberman (ID-Conn.) on Tuesday emerged as one of President Barack Obama’s most critical allies in the debate over the administration’s new strategy for Afghanistan.

“From everything I’ve heard, the president has made the right decision— in his war strategy, Lieberman said prior to Obama’s speech to the nation Tuesday from the U.S. Military Academy at West Point.

Lieberman had criticized Obama’s pace in announcing his strategy for the war-torn region — and he has often been a thorn in the president’s side on issues such as health care reform over the past year.

But on Tuesday his blessing was an important one as the new strategy for Afghanistan agitated Obama’s liberal allies and was slow to gain any traction among Republicans.

Lieberman advised the president not to impose “an explicit deadline to get our troops out, because that undermines the mission.— He offered his support to the idea of a war surtax to pay for the effort and added that “some mention of a timeline or goal is OK.—

White House adviser David Axelrod, in a brief interview with Roll Call, appeared to suggest that the president does not support a direct tax, saying the costs need to be addressed “in the context of the fiscal challenges we face and not as a standalone issue.—

Lieberman’s remarks stood in stark contrast to those by his longtime ally, Sen. John McCain (R-Ariz.). McCain said he was “pleased— with Obama’s plan to nearly triple the number of U.S. troops in Afghanistan but held firm against placing any kind of timeline for withdrawal.

“I do not believe we should have a date certain. … We should have a goal of being out the day after tomorrow, but it’s dictated by conditions on the ground,— said McCain, ranking member of the Armed Services Committee.

“As we succeed, as the surge succeeded, as this strategy, I believe, will succeed, then there will be a conditions-based situation where we can withdraw the troops,— added McCain, one of 31 lawmakers who met with Obama hours before his address to the nation.

In his Tuesday night address, Obama shed light on one of the most contentious aspects of his strategy: the deployment of 30,000 more U.S. troops in the first part of 2010.

This is “the fastest pace possible, so that they can target the insurgency and secure key population centers. … They will help create the conditions for the United States to transfer responsibility to the Afghans,— Obama said. He said he is “confident— that other countries will commit troops in the coming weeks and that he planned to begin transferring U.S. troops out of Afghanistan in July 2011.

The slight divergence between McCain and Lieberman is the result of “a new and different situation that doesn’t fit into past molds,— a senior Democratic aide suggested.

“Things have changed so dramatically on the ground and in leadership in this country that it’s jumbled everything up,— the aide said, suggesting that the usual alliance among Lieberman, McCain and Sen. Lindsey Graham (R-S.C.) on defense issues in recent years has shifted in the months since Obama took office.

“The expected answers on these issues aren’t the same,— the aide said. “So the legislative coalition to move this along is unclear.—

Senate Armed Services Chairman Carl Levin (D-Mich.) hailed the notion of a timeline while stopping short of a full endorsement, simply declaring “the right mission is to train the Afghans for their own security.—

One of Obama’s most vocal critics on the war, Sen. Bernie Sanders (I-Vt.), ripped into Obama’s plan for more troops and threatened to take action against it.

“With a quarter of our kids living on food stamps, I am not sympathetic to spending $100 billion on Afghanistan, plus what we’re spending in Iraq,— Sanders said. But asked how he could prevent troop increases, he said, “Well, we’re going to work on that, I guess.—

Obama has been testing his relationship with liberals for months, but his war plan now puts him at odds with some of the more influential players on the Hill — namely, those who control the purse strings.

House Appropriations Chairman David Obey (D-Wis.), who vowed in May to finance all future Afghanistan war spending in the regular budget process, has been pushing legislation that calls for a war surtax to cover the estimated $1 trillion cost of maintaining a counterinsurgency effort in Afghanistan over the next decade.

While his bill is largely symbolic and not expected to gain traction, it has drawn a powerful cadre of co-sponsors: Appropriations Subcommittee on Defense Chairman John Murtha (D-Pa.), Democratic Caucus Chairman John Larson (Conn.) and Financial Services Chairman Barney Frank (D-Mass.).

“The only people who’ve paid any price for our military involvement in Iraq and Afghanistan are our military families. We believe that if this war is to be fought, it’s only fair that everyone share the burden. That’s why we are offering legislation to impose a graduated surtax so that the cost of the war is not borrowed,— they said in a statement.

Congress won’t have to vote on giving Obama more funds for at least another six months.

But Obama will need Obey and Murtha on his side if he hopes to secure funding for his war strategy.

And with liberals uniformly opposed to more troop increases, Obama has to deliver a strong sales pitch to fiscally conservative Democrats leery of adding billions more to the deficit.

Rep. Jane Harman (D-Calif.), a Blue Dog whose voice carries weight on homeland security and defense matters, signaled Tuesday that Obama will have a hard time selling the idea that 30,000 more U.S. troops will increase the likelihood of success in the region.

“Expanding our military footprint in Afghanistan is a mistake,— Harman said in a statement. “A larger occupation gives the Taliban an enhanced recruiting tool, continues the dependency of Afghan fighters on our superior training and logistics, and commits scarce U.S. resources … at a time when other counterterrorism challenges … appear more urgent.—

Harman, a former Pentagon aide, said the situation in Afghanistan carries the “eerie echoes of Vietnam— and cited a crucial 1965 memo from National Security Adviser McGeorge Bundy to President Lyndon Johnson about there still being time to turn around the deteriorating situation in Vietnam.

“Bundy turned out to be wrong, and I think a troop buildup as part of an otherwise careful and thoughtful strategy is also wrong,— Harman said.