Or maybe — gulp — he really does believe that Iraq is still fixable,
There is a lot that has been fixed, is getting fixed, and that could be fixed, still.
that Maliki will soon emerge as a unifying national leader,
When people tire of violence, they will want a national, unifying leader, if not before. When the government is able to defend itself on its own terms (i.e. have a more full command of Iraqi troops), that also may be a catalyst for change. One may not like that change or its modus, but ...
that American troops will manage to calm a civil war,
Sufficient American troops (and an empowered judiciary) certainly can forestall an escalating cycle of reprisal killings. Either those fighting will exhaust themselves in a struggle by eventually realizing that they cannot consolidate the small gains they make in 'reprisal', that they cannot gain anything long-term by excalting and getting their neighbors involved, or that they can reach some interim political compromise (and start to work together, despite rivalry and animosity).
that trained Iraqi troops will fight for a united democratic government rather than for sect or tribe or vengeance.
In some instances, they already are (the fifth division isn't the whole story). The question is whether so-much can be brought to scale and how quickly, given the other inter-dependent tasks to complete (and the failure to prioritize this task from the outset).