This is quite the unexpected blow, but I submit that Americans have a long-standing tradition of being unwilling to take certain jobs, and that this should have been expected. One might say that this country is founded on the idea that all men should be free to choose the jobs they don't want to do.
Unlike everyone else that's complaining about this issue, though, I have a solution. Instead of a single "War Czar," we just need to create a "Bureau of War" and staff it with the one group of people who have a long-standing tradition of accepting the jobs the rest of us Americans don't want to do: illegal Mexican immigrants.
This solves both the Czar problem and the immigration/amnesty problem, because all so-called "illegal" Mexican immigrants will now be government employees, entitling them to benefits like healthcare, taxation, and the always popular "not getting kicked out of the country." Having seven million "War Czars" ought to get things in Iraq nailed down at least seven million times faster than the single "War Czar" that we're currently unable to find, so this proposition wins all around.
Also: taking into account the popular sterotypes of both Mexicans and government workers, this pairing seems like a pretty good match to me.