What the Democrat strategy should be now
The Democrats should target Cheney for impeachment, and use the threat of hearings against Bush to secure promises from him he won't veto legislation. They didn't promise not to impeach Cheney, and as one of the most disliked politicians in America, they could do so without meaningful consequences. Sure the 22 percent of knuckle dragging hillbillies who support the right no matter what are going to be mad, but so what. The more shrill they grow, the worse it is for the GOP in 2008; their shrieking and railings will only serve as a reminder of the 2006 slap down and why it happened.
If the Democrats are smart, they are now in a position to play a brutally effective game of political Jenga, carefully pulling out administration pieces until the President remains alone, marked and teetering, right before the election. They have the opportunity of the century to pass legislation without fear of the veto pen if only they are ruthless and smart enough to use the unseen power of Bush's multiple criminal acts to secure his cooperation. His cooperation protects him, but destroys the GOP machine.
Impeaching Cheney first, would also insure that should they decide to impeach Bush at some point, Cheney could not replace him. But so much more can potentially be accomplished by going to Bush and offering to leave him alone so long as he cooperates with enacting the legislation. They may even be able to force Bush to rightly take responsibility for his lost war and preclude the GOP attempting to tar the Democrats with it.
Call it blackmail if you want because it is, but when dealing with someone who's committed serious multiple crimes from a position of legal authority, it's perfectly legal, and they'd be damned fools not to use the power. If they do everything right, they can pick off the entire administration one at a time, while forcing Bush to pass their agenda. The base of the GOP will be so angry at Bush for his cooperation by the time they're done with him, Hillary might actually be electable.
That is what I would try to do, were I the new majority leader.