Politicians have gone further, making sure to point out that they support spending bills that would provide the troops with armor, health insurance, etc. as proof that they support the armed services personnel themselves. But these same politicians want to not support the war itself. The problem here is that if you give the troops the means to survive in a hostile land, you're almost automatically giving those same troops the ability to continue to fight the war they're being asked to fight, which in turns means you've done nothing to take away that ability from the politicians making use of the military. There's no way to win this argument: if you try to take away funding, you'll be accused of putting soldiers unnecessarily at risk. You might think that the argument could also be made that those who keep our soldiers at war are the ones putting them at risk, but there's the whole "status-quo" side to it too -- the soldiers are already out there, so whosoever makes any changes is responsible for the consequences of those changes. At least that's the idea.
Troops as hostages
Let's try analyzing the situation within the framework of the "hostage situation" analogy.
As a hostage-taker, your main goals are to: project the image of a reasonable person, and remove from the equation any discussion of how the situation began. You want to firmly seat your opponents in front of a simple problem, where things are the way they are (no need to talk about how they got that way), and the future is predictable (thus the "reasonable person" image.) In that situation, the opponent is forced to think only of his goals, his means, and the direct correlation between his actions and the consequences upon the hostages -- the hostage-taker is as much a part of the situation as gravity, a mere mathematical equation. Guilt becomes automatic for the public at large, and for the hostages themselves, there's a feeling that you're not really the bad guy, the public is in the wrong for not coming to their rescue (Stockholm syndrome;) it's as if they'd fallen in a well, and you're just a well (nothing to get angry about) and the public, debating whether or not to give in to the demands, are incomprehensibly unhelpful.
Now if we take that idea and apply it to our present situation, we have troops held hostage over-seas, who need our help, and who won't blame the President for putting them in that situation because he's managed to pull himself out of the equation ("don't think about how we got here, just think about what you're going to do about it"), and a Congress that can't easily refuse to send money (aid) to the troops, because doing so would further alienate them.
Now consider that we have, in general, a policy of not agreeing to the demands of hostage-takers. For obvious reasons, we can't give the appearance of being weak, or we'll be taken advantage of at every opportunity. Yet in this situation, it's difficult for the Congress to say, defiantly, that they won't be bullied around by the President, that if that means harm must come to the troops, then so be it -- to do otherwise would be to authorize future presidents to continually put troops in harm's way as they please, then ask the Congress to further support the operation or be accused of abandoning our personnel in a dangerous situation.
Just following orders
You'll further find that it's hard to support the troops, and praise them for how effectively they've done their job, when you disagree with what they're being ordered to do. The Nuremberg trials after WW2 displayed an aversion to the concept that acting under orders exempts anyone from prosecution for their actions. Can we praise someone for being an effective murderer, when the murder itself is unrighteous? Can we continue this lie that our troops have no choice but to follow orders? But at the same time, what would happen if we did suggest that our troops should fail to obey? The next time our government needed them in a conflict, that call to rebellion would come back to bite us.
Doing the right thing
It's got to be helpful for a soldier to believe that what he or she's doing is the right thing to do, in order to do it effectively. Can you imagine going into battle, not believing that your side was right? That your only reasons for fighting were your own safety, and that of your friends in combat? No wonder we talk about troop morale being linked to what the public at large has to say about the war -- knowing that half the people back home think that what you're doing, day in, day out, under harsh conditions, at the edge of your conscience, risking your life, is the wrong thing to be doing ... that's got to be hard. We don't want that for our soldiers. We don't want to put them at more risk because they pause to doubt, mid-battle, what they're being asked to do. But can that be logical justification for not questioning the war? It's hard to have a useful debate without doing so out-loud.
Dying in vain
I've heard troops talk of staying in Iraq to finish the job the fallen soldiers had begun, as a way of honoring their memory. We really don't want our troops dying for a bad cause; once they've died, we can't seem to bring ourselves to tell them, after the fact, that what they died for wasn't worth it. In particular, if we take the idea that the Congress authorized the war (note: authorizing is not the same as starting, it just means you don't end it) then for them to later change their minds is downright insulting: troops are not toys, we can't just send them off on a whim then decide to cancel the whole thing.
On the other hand, we have this concept that continuing down the wrong path, once recognized, is more foolish than starting down it in the first place. Why is it so difficult for us to admit, openly, that we started a war for the wrong reasons, and that we should take a fresh look at our goals and our means -- not simply continue what we've started for the sake of honoring the dead, and hiding our shame at having made a bad decision. I'm not saying that the solution is to just pull troops back and end the occupation overnight; I don't know what the solution really is. I simply know that the arguments being used for keeping us there, as-is, are logically wrong (but emotionally powerful.) Even if we do, in the end, make the right decision, it's hard to brag about it if you came to the right conclusion the wrong way.
Let's honor the dead for having served our nation bravely, right or wrong, and ask the living to do what the nation now thinks is the right thing to do, regardless of past decisions. Every day is a new day.