To what problem? The administration is attemtping to solve the problem of the proliferation of terrorism aimed at Americans from the Middle East. Bush is putting it all on the line because he believes that to do nothing is a much more dangerous proposition.
If you are looking for utopia, you will be chasing windmills forever. If you are looking for the most realistic option, it is to turn over authority to an interim government (before it is thoroughly tainted by nationalist accusations of collaboration) and undertake a fast time table for withdrawal.
Which would make the entire exercise undertaken and seen through by young Americans in uniform futile.
No, the jihadists are on the ropes. If Bush can stabilise Iraq with some sort of democracy it may spread seeds. Very difficult I know.
"Some sort of democracy" means exactly what Captain Kirk has proposed. Military occupation with appointed colaborators has nothing to do with any "sort of democracy".