We've seen in the Terri Schiavo case that the Republican-dominated House and Senate can move quickly and decisively - albeit foolishly in that particular case - when there's an issue afoot that they really care about.
Things aren't working that way when it comes to Bush's grand adventure in Mesopotamia. Historian James Carter asks in this article: Is Congress AWOL on Iraq? History News Network 03/07/05.
The short answer: yes.
Carter gives a good, brief summary of the Congressional investigations that took place in the 1960s into the conduct of the Vietnam War. During the Johnson administration, these involved a Democratic Congress holding hearings that often embarrassed the Democratic President, because they considered the issue sufficiently important to override partisan considerations to a significant extent.
He also summarizes how today's Republican Congress is handling things:
The fact is that the committees of jurisdiction have so far refused to conduct proper investigations because they might shed some unfavorable light on the administration’s debacle in Iraq. While several congressional committees have conducted investigations into the much more politically useful oil-for-food program scandal, not a single hearing has been held to examine the mismanagement, corruption and allegations of outright fraud of its successor, the Development Fund for Iraq (DFI), an entity the U.S. government has invested with billions of taxpayer dollars and also controls. Those involved charge the DFI has misappropriated many millions and there is little or no oversight or record keeping. The majority-controlled congressional committees have so far refused to conduct legitimate hearings that would give these matters the proper venue and the proper visibility.
These trends seem likely to continue. Bush administration officials are increasingly bold in their refusal to submit to the Congress. A few days following the above ad-hoc hearings, Secretary of Defense Rumsfeld refused to give details, refused to answer questions and abruptly collected his papers and left hearings before the House Armed Service Committee.
Maybe if the Christian Right hears that abortions are becoming more frequent in Iraq, their friends in Congress will start to look at the conduct of the Iraq War more closely.