WASHINGTON – Facing growing budget pressure and an increasingly skeptical public, Congress's appetite to continue funding the war in Afghanistan appears to be diminishing.

The House on Thursday voted 321-93 against withdrawal of U.S. forces from Afghanistan by the end of 2011 -- although a similar measure was rejected last year by a larger margin of 365-65. Eight Republicans and 85 Democrats voted for the resolution, which was sponsored by Reps. Dennis Kucinich (D-OH), Walter Jones (R-NC) and Ron Paul (R-TX).

The increased support for withdrawal -- despite Republicans taking over the House -- reflects the public's pessimism regarding the endgame of the ten-year Afghan occupation, America's longest ever war.

"Are we willing to spend another trillion dollars on a war for which there isn't any exit plan? Where we haven't defined our mission?" Kucinich said on the floor before the vote, highlighting the war's strain on the budget. "We can trim the federal budget of more than $100 billion in out of control spending."

Though still a minority in Congress, lawmakers who voted for the bill are backed by public sentiments. A record-high two thirds of Americans no longer believe the war is worth finding, according to an ABC News/Washington Post poll this week.

Army Gen. David Petraeus, the top U.S. commander in Afghanistan, warned in stark terms that passage of the measure would undermine NATO's mission to root out the Taliban and al Qaeda.

"The Taliban and al Qaeda obviously would trumpet this as a victory, as a success," Petraeus said Wednesday in a committee hearing. "Needless to say, it would completely undermine everything that our troopers have fought so much for and sacrificed so much for."

The Obama administration maintains that U.S troops will begin a staged withdrawal from Afghanistan this July and has set a tentative deadline of 2014 for an end to combat operations.

The bill's sponsors say withdrawal can't come soon enough.  They and other critics charge that the definition of success has been so blurred as to become meaningless, fretting that the U.S. is mired in a quagmire with no end in sight.

The Obama administration hasn't budged on its commitment to the war, characterizing it as vital to U.S. national security interests. A preemptive withdrawal, officials argue, would undermine the moderate coalition and strengthen the Taliban insurgency.

Yet even among top Republicans, who have so far been resoundingly supportive of the war, signs of discontentment are emerging.

Mississippi Gov. Haley Barbor (R), who is eying a presidential run in 2012, on Tuesday questioned the feasibility of the Afghan mission and said "we need to look at" the possibility of decreasing troops, according to Politico.

Watch Kucinich's floor speech, uploaded by CBS News.