Ambassador Crocker and General Petraeus are actually working at cross-purposes. Petraeus's military 'successes' and local initiatives come at the expense of the national political track, not in support of it...
Crocker's job is to encourage political reconciliation at the national level, which has been the Bush administration's stated goal from the start and which was the declared goal of the 'surge'...Petraeus's strategy thus far has been to work at the local level. His signature initiative to date, the arming and tactical alignment with Sunni tribes and former insurgents, largely ignores the Iraqi state.
They aren't working at cross-purposes, exactly. By appealing to Iraqis more directly, Petraeus is moving the entire table.
It's a little like the medieval practice of circuit courts: by demonstrating that Iraqis can get better results at the hands of the Americans rather than their own government, the U.S. increases its credibility among the populace, just as English citizens' discovery that they received better justice at the hands of the King's servants' rather than their local lords increased loyalty to the King.
Maliki can no longer drive out the Sunni populace by withholding state funds from them and turning a blind eye (at best) to the Shia militias and the Al-Qaeda groups used to justify their existence. The root problem, I guess, is in the Iraqi Arab winner-take-all approach to government, no matter if it is democratic or not. Just look at how a Saddam-era law was revived to protect government ministers AND their entourage from prying eyes, once again enabling high-level corruption.
If Maliki and his ilk refuse to change their purposes very soon, answers to these problems can only be found at the political, not diplomatic, level. Possibly the U.S. could help by taking a more active role in the Iraqi political process, openly pointing out Maliki's failures and proposing that Iraqis support a government that truly embraces the country, rather than sectarian desires. Perhaps the U.S. can encourage the development of local leaders, especially those who have become prominent in the wake of The Surge. These can then band together and, because of their popularity, apply pressure to the "national" government, or start a national campaign themselves.
This makes the success of The Surge more important than ever. Not only must Al-Qaeda be dealt with, but the Shia militants as well, to better forestall any campaign to silence or assassinate moderate Shia leaders by militant extremists of any stripe.