This is an idea I thought I'd try and float more formally somewhere, but that may have to wait. The idea is that there's no reason why the majority party in Congress, or any other legislative body, should have exclusive control in overseeing the executive branch. While winning the majority vote rightly gives that party control over the legislative agenda to put its ideas into effect, oversight is a different matter.
My idea is each congressional committee that has an oversight role would split the oversight functions between the majority and minority party. The majority gets more hours to hold hearings and issue subpoenas, but not exclusive control. This way the advantage of having the executive and legislative branches controlled by the same party - a better chance at carrying out a legislative agenda - still has real oversight, something sadly missing in Congress for the last six years.
It would also have the effect of encouraging competition between the parties over which one does more effective oversight. It would be harder for Republican congressmen to coddle the Bush administration if on a regular basis they turned the gavel over to Democrats who actually asked hard questions. Maybe the Republicans would start stepping up to the plate.
Finally, I think it's a good idea for either Republicans or Democrats. All of them think they'll be in Congress for a while. Rather than become nearly irrelevant when they're in a minority, this could give them a bit of power in the lean years.
I don't see much of a disadvantage. But I always like my ideas.