Yale law professor Jack Balkin makes an argument that is very commonly heard these days: that the separation of powers has broken down and presidents can engage in warfare with little or no congressional support:
The sad lesson of the past year is that the modern Presidency-- armed with control over military intelligence and a large standing army-- can have its way in matters of war even if the President's policies are very unpopular, and there is very little Congress can do to stop it.
This lesson should be abstracted from one's feelings about the current occupant of the White House. George W. Bush is a failure-- I won't mince words-- but even a failed President can do pretty much what he wants in war given the way our constitutional system has developed following the Second World War and the rise of the National Security State.
I disagree. In fact, it is very difficult for a president to either initiate or continue a military conflict without fairly strong congressional backing. And the evidence of the last 60 years proves it.
I. Initiating War.
Let's start with war initiation. Virtually every major military action undertaken by the US since World War II has either been formally authorized by strong congressional majorities in advance (Vietnam, both Iraq Wars, Afghanistan), or enjoyed strong congressional support without a prior formal vote, though often there was an authorizing vote after the fact (Korea, both Lebanon interventions, Grenada, Somalia, Haiti). There is only one noteworthy exception to this rule: President Clinton's 1999 military action in Kosovo, which was opposed by most congressional Republicans. Yet even this case partly validates the rule. Knowing that congressional support was severely limited, Clinton took account of this political reality and carefully limited the scale of US involvement and especially US casualties (which didn't include a single combat fatality).
Setting aside constitutional considerations, there are good political reasons for presidential reluctance to initiate war without congressional support. If the war goes badly, the president will be hung out to dry politically and suffer a severe backlash. Moreover, as discussed below, Congress can use the spending power to stop a war it opposes dead in its tracks. With congressional support, by contrast, the president can shift some of the blame to Congress and make it difficult for the opposition party to blame him by pointing to the fact that their congressional representatives supported the war as well (a gambit President Bush used to great effect against John Kerry in 2004).
II. Continuing War in the Face of Congressional Opposition.
Even if presidents can't get away with starting a war without strong congressional support, perhaps they can get away with continuing it long past the point that Congress would like to end it. This is what many observers, including Balkin, believe Bush has done over the last year. The problem with this theory is that Congress does in fact have the power to stop a war at any time: it can do so simply by refusing to vote continued funding for it. This is true not only under my fairly expansive view of Congressional war powers, but even under John Yoo's extremely restrictive one. I would further argue that Congress also has broad authority to regulate military action in other ways. But even if that's not true, the uncontested spending power is itself sufficient to stop any war that Congress truly wants to end. The Iraq War could not continue for long without constant infusions of money.
Jack Balkin notes that the president can veto congressional efforts to stop a war. However, the power to deny funding is effectively veto proof, since Congress can exercise it simply by refusing to vote the money in the first place.
Why, then, have congressional Democrats failed to stop the war in Iraq? My guess is that, however much they dislike continuation of the war, they fear a precipitous withdrawal even more. Such a step could well cause a foreign policy disaster for the country and a political disaster for the Democrats themselves (because they will get a large share of the blame). On the other hand, the combination of continuation of the War with continued harsh criticism of Bush avoids this scenario, while enabling the Democrats to blame Bush (with considerable justice) for any failures on the ground. If congressional Democrats could agree on an alternative to Bush's strategy that they believe would both avoid immediate disaster and end the war fairly soon, they could very likely use the spending power to force Bush to accept it. But they don't have such an alternative, or at least most of them don't think they do. The war continues not because Bush - or any president - "can do pretty much what he wants in war," but because the congressional majority doesn't really want to use its power to stop him from doing it.
UPDATE: Some scholars add the additional twist that Congress' power to stop a war is difficult to exercise because, once war is initiated, Congress might legitimately prefer to victory to defeat, even if it would ultimately have preferred never to have started the war in the first place. Perhaps the congressional majority has a rank order of preferences of 1) no war (perhaps because they consider the price of victory to be too high), 2) an overexpensive victory, 3) defeat. But once the president initiates hostilities, only options 2 and 3 are still on the table. This argument would have great force if presidents really were able to start wars without congressional support. In fact, however, they have been unable or at least unwilling to do so.
UPDATE #2: Several commenters argue that the Democrats couldn't really defund the Iraq War without defunding the entire Department of Defense (since the Bush Administration could otherwise try to use funds allocated for general DoD purposes to continue the war). This is an interesting point, but I don't think it withstands scrutiny. The Democrats have at least two other ways to defund the war. First, they could refuse to authorize DoD spending bills without attaching riders forbidding use of the funds in Iraq (or at least strictly limiting that use to funds needed to effectuate a withdrawal). That approach would court a confrontation with Bush (who would threaten to veto). But the Democrats would have a good shot at winning that confrontation, in light of Bush's low public standing and that of the war.
Moreover, as a practical matter, waging the Iraq war requires numerous appropriations for specific equipment, payments to contractors, spending on Iraqi support personnel etc. of a type needed in Iraq, but not needed in comparable quantities for other military activities to continue elsewhere. For example, the war requires a variety of specialized equipment needed to operate in Iraq's desert environment. Congress could push through a bill excluding these items or strictly limiting their quantity to something approaching the amount needed to implement a relatively fast withdrawal.
No doubt those more expert in the federal budget process than I am could think of other ways for Congress to use the spending power without having to defund the military completely.