We know Bush is virtually certain to order an increase in US troop strength in Iraq. We know that he's been strongly advised against doing so, but that if he does proceed with such a plan, it must have a clearly defined purpose. Perhaps he does have a defined purpose in mind - killing or capturing the guy that Newsweek called the most dangerous man in Iraq.
In theory, Iraq now has a constitutional government, and the Administration line is that our forces are helping the Iraqi people develop a stable government under that constitution. I'd have to assume that Bush and friends have taken a look at Sadr's political and military power, a religious/ethnically-based sort of "people power" not derived in any way from the constitution, and have asked how they could ever get to the "victory" they're longing so desperately to achieve so long as Sadr maintains his extra-constitutional stranglehold over Prime Minister Maliki and Iraqi politics. So "Why not do something truly bold?," they may ask; with these extra troops, let's do whatever it takes to fight a path into Sadr City, neutralize this giant thorn in our side, and clearly establish that Uncle Sam is still the sheriff in Baghdad. The image of American impotence would get an extreme makeover, right?
Yes, it would be bloody, the lives of many U.S. troops and innocent Shiite civilians would likely be lost, and our friend Maliki wouldn't be happy (in public, at least); moreover, we really can't say just how it would all turn out in the end, what with so many other aspiring militia leaders itching to lay claim to the "most dangerous" title. In addition, many Shiite followers of Sadr would hate our guts forevermore. The history of the last four years of the Bush administration clearly demonstrates, however, that such considerations are not deemed insurmountable obstacles when urgent action to remove a foreign leader is the order of the day. Bush & Co. would be able to say "See - we didn't just 'stay the course', we really went the extra mile to protect Iraq's blossoming democracy."
As outlandish as it seems, I'm afraid that the thinking in the Bush/Cheney circle is such that this scenario is hardly implausible.