In fact, in light of the internet and the preponderance of evidence already out implicating Bushco's having lied to Congress to coerce them to declare war, it is compulsory for Congress to pursue the Executive branch if the citizens it represents call for it.
But first I guess, they technically need to impeach Bush and Cheney...then they can go after them as the common criminals they appear to be.
As to complying with the World Court, it seems that there is a law morally compelling Congress to cooperate with regards to the Bushco trials:
It says they have the power to, not that they must. But in order to protect the US citizenry en masse, from backlash of atrocities committed unjustly to other nations by the harbored-fugitives Bushco, Congress is really mandated to prosecute them, because Congress is in charge of maintaining protective services for the citizenry of the US.
Laws like these are somewhat broad and open to interpretation. It could be interpreted that Congress might choose to repel invasions (could be interpreted as "random acts of terrorism against the citizenry" ) by holding it's nefarious officers or former officers of state to prosecution for acts deemed to agitate compelling and well-founded worldwide hostilities towards the citizenry. So if the Hague finds Bushco blatantly guilty of acts of unforgivable and illegal atrocities within the World Court, Congress may then act on behalf of securing the safety of its citizenry from predictable backlashes by cooperating with extradition and sentencing of the criminal element responsible.
In fact, I would think it would be mandated?
