Republicans talk of political stability in Iraq created by a calmer security environment, which is facilitated by American military presence. Democrats want to force Iraqi political reconciliation by signaling to the Iraqi government that American forces won't be around forever by threatening a withdrawal of troops.
At this point, the basic aim of both parties is to convince Iraqi political parties that it is within their national interest to work together. The thinking goes that once all sides are locked into their positions within the government, the fighting will cease because militia bosses and their political patrons will be content with their place in the pecking order.
This logic fails to accept that the various warring parties do not want to resolve their centuries of religious, political, and ethnic differences, unless their sect is on top. Furthermore, this logic fails to accept that we are no longer in a "war". Instead, we should be simultaneously conducting a long-term police action along with deft diplomatic maneuvering designed to get a foreign government to act in American interests.
Let's then admit that diplomacy should take precedence over security, because political stability is the only condition under which we'll ever leave. And, by definition, diplomacy is using reward and punishment (or, "carrots and sticks" to use diplomatic vernacular) in order to get someone to act in your self interest.
What, then, is the carrot and stick that the US proposes to the Iraqis?
From the Republican perspective, there is neither: The Bush administration is obviously advocating that the sides reconcile, but without tangible motivation to do so either in terms of political or financial reward, without obvious punishment if they don't. No carrot, no stick, no progress.
From the Democrat perspective, at least there's a (proposed) stick: if the sides don't reconcile, they propose we leave. In other words, failure to make political progress will be punished by even greater levels of insecurity. Where is the Democrat carrot? If the Democrats are serious about a different course in Iraq, then there has to be a motivating factor for the Iraqis to work together.
One guaranteed carrot is exactly the opposite of what the Democrats have proposed: Turn our withdrawal from a stick into a carrot. If the sides take steps to pass legislation, then guarantee that each milestone achieved will be guaranteed to be met by a predetermined withdrawal of troops. It's unquestionable that the political parties' constituents want the US to go home. Make that promise, but attach it to progress.
Here's where the refocused stick comes in: taking the fight to them. Promise complete destruction without progress, and then show them by attaching punishment to lack of progress.
But also, solutions start by talking to the people who matter: the extremist warlords, not the government. Find out what they want, then work on a way to give it to them within an acceptable American framework. Peace in Northern Ireland finally looks like it's about to work because the erstwhile extremists -- Gerry Adams and Ian Paisley -- sat down and agreed to terms to live together. On the other hand, 2000's near Israel-Palestine Camp David Summit failed because Arafat couldn't placate the extremists back home.