The top level goal of the US military's COIN (counter-insurgency) doctrine, as described in the much ballyhooed manual, is to maximize the legitimacy of the host government. Everything in the manual's doctrine is slaved to that goal. So, under this rubric, Iraqi PM Maliki's attempt to take control of Basra would be completely supported (although there might be some dispute over tactics/methods/timing).
However, the US military isn't following its published COIN doctrine. Instead, it's following the dictates of open source counter-insurgency. This doctrine, still unarticulated and very far from officially condoned by the US military (policy lags theory and theory lags practice), has a top level goal of stability, even if it at the expense of the host government's legitimacy. To achieve stability, deals or truces are made with non-state groups (formed around strong primary loyalties like tribalism, religion, ethnicity, clan, and neighborhood). The benefits of these deals and truces are clear, if they reduce violence they get a degree of autonomy and in some cases money, weapons, and training. As we have seen over the last year, it works.Open source counter-insurgency can work indefinitely if the host government remains passive (although at the cost of a badly functioning hollow state and lots of money). However, if the host government calls the bluff (the gap between "policy" and "practice") and begins to roll back the autonomy awarded to competitive non-state groups, the entire effort will shatter. Maliki is doing this now with his excursion into Basra. As a result, US policy in Iraq is now being gored by the horns of a dilemma. The US appears to be unable to decide which bad option to select: support Maliki and the country collapses into an orgy of violence - or - let him fail and the Iraqi government loses its remaining legitimacy and cohesion.