The media would have tried, but Bush has the opportunity to bypass the media and speak directly to the American public if he chooses. And remember, regardless of the media's view 90% of Americans favor Bush's handling of the war. Bush would merely need to come out and speak reasonably about how, "We may have our differences on domestic policy, but we must present a united front to the world unless we want a repeat of 9/11." That would have sent Daschle scampering back to his hole.
And if you really think we could have demolished Daschle, simple as that, we'd have done so. It just couldn't be done.