Whether or not the US has "won" in Iraq yet is a bit unclear--it depends who you ask what the objectives are. And, frankly, I don't think that anyone quite knows the answer, even if they sit down and give you a list of said objectives. But if you imagine the most broad, liberal, and generous of objective lists, it looks like the US is a few key steps away from making Iraq a beacon of American power, determination, and values.
What are the primary obstacles? To be certain, there is corruption, major factionalism, poverty and displacement, security holes, Iranian influence, bureaucratic ineffectiveness. But, frankly, I think the linchpin here will be the Arab-Kurd negotiation process over the status (and size) of Iraqi Kurdistan. Continued ambiguity on the topic will be a major hangup for the resolution of all these other problems, and is the single most likely problem in all of Iraq to cause major destabilization of the regime.
The Arab-Kurd conflict in Iraq is a rather frustrating problem I have lamented a number of times in the past--it has been highly unclear to me exactly how Iraq was going to solve its Kurdistan problem. Kurdistan had both the power and the motive to keep pushing the central government for a greater advantage. As long as its future projections for relative power were good, a stable state could not be reached.
But the strangest of butterfly effects may be taking place. As you probably know, Turkey is hot for a bid into the EU, and has been struggling immensely to realize said bid. There are many obstacles in Turkey's way, the least of which is not racism and Islamophobia in many parts of Europe. More legitimate problems, like governmental stability and human rights questions, have kept it out, as well.
The Turks have taken their rebuffs in stride, carefully noting any concrete objections in order to try to annihilate them and (seemingly) legitimize their bid for EU ascendancy. At the top of this list of objections has been the Turkish treatment of their Kurdish minority. In a 25-year-long low-intensity war to keep the province from breaking away, the Turks have taken great measures to "Turkify" their Kurdish southeast. Banning of wearing Kurdish clothing, teaching Kurdish in school, Kurdish-language television, and Kurdish cultural/national symbols, as well as a bold official renaming of places in Kurdistan to Turkish names have been part of an overall effort that has been (somewhat fairly) called "Cultural Genocide." Frankly, it has also been a failed policy, and has more likely bolstered resistance to integration rather than eroded it.
In a rather stunning about-face, the ruling coalition in Turkey has offered a rather generous peace deal, which includes (among other things) a restoration of the Kurdish right to express a cultural identity (including television, school, clothing, etc). While certainly far from an easy fix, the overture has certainly caused the peace process to gain a great deal of momentum. In an equally stunning reply gesture, 8 PKK members from Iraq crossed the border and laid down their weapons to help cooperate with the peace process.
Obviously, there will be implications in Iraq. The decision clearly seems to be having some impact on Kurdish nationalist motivation--if the PKK (in Iraq, even!) is beginning to walk across the border and lay down arms, the organization as a whole clearly has a lot less steam to fight than it used to. Because Kurds in Iraq are probably approximately as concerned with Kurds in Turkey as other Kurds in Iraq, seeing Turkish Kurds accept a fruitful and just peace process will certainly dampen the "us versus them" mentality that has dominated ultranationalist Kurds since the early 20th century. Furthermore, if the peace process works, government control will be restored to Southeast Turkey, meaning that Iraqi Kurdish fighting groups will no longer have a porous border behind which they can rest, regroup, rearm, etc. They will have lost a key (and much larger) ally in the struggle with Iraqi Arabs, leading to decreased military power and decreased bargaining power.
With deflated motivation and ability (assuming the peace process is as rosy as everyone hopes), Iraqi Kurds are likely to realize that their future negotiating prospects are going to only be going down. This implies that today is the peak of Kurdish power in Iraq (assuming central government power will not also decrease). Any good negotiations theory says that you should (and do in fact tend to) negotiate for a settlement when at your peak of relative power. The Iraqi central government could try to drag out the negotiating process to bargain from a position of higher power later, but if they're smart, they'll want to get this done and over with without giving up too much, such that they can move on to other big problems.
Assuming that these dominoes do fall and the Kurds find a framework in which to get along with the Arab central government, a whole host of problems are going to be solved. First, Kurd-controlled and Baghdad-controlled troops will no longer be squaring off with each other--they can spend their time hunting down the remnants of al-Qaeda that (intuitively) are most dominant in the fuzzy border between the Kurdistan Autonomous Region and the rest of Iraq. Furthermore, a settlement will include election agreements, which should put a dent in factionalism and volatility in Iraqi politics, which should allow more stable ruling coalitions to actually spend political capital to tackle big problems (like corruption, power supply, IDPs, security, etc). Finally, and perhaps most tantalizingly, an agreement will likely include an oil deal, allowing Iraq's vast oil riches to finally be fully exploited--and for both governments to get significant cuts that should fund a strong Army, a strong reconstruction process, and a healthy health/education department (why this is not the case in many other oil-rich states is a very long story, but for a number of reasons I think Iraq is unlikely to fall as far into the dark pits of inefficiency, corruption, and central planning that plague many other oil states).
I don't quite mean to imply that the Turkish-Kurdish peace will will be a cure-all in Iraq. But if the dominoes fall as I think they will, it will remove what is perhaps the biggest obstacle to the Iraqi central government effectively dealing with its top domestic issues. If those can get chugging along, then the Americans can begin to feel pretty secure about having achieved even the most ambitious and extensive goal list in Iraq.