Based on his campaign postering regarding how he will keep doing the same things he has always done with regards to the war in Iraq, detainees, etc., it appears that when the Democrats take over the House, Bush will adopt a Two Pronged Strategy.
On the one hand Bush will continue to do more of the same of what he has been doing, despite any attempts by Democrats to criticize and exercise oversight over Bush and his failed policies with regards to Iraq, taxes, civil liberties, the war on terror. As with judicial rulings against the administration which Bush chose to simply ignore or with his having no mandate after the 2000 election, Bush's strategy has consistently been to ignore anything opposing his policies or anything dictating that he moderate his policies or reach out to the other side. Instead, he choses to rule as if God annoited him King of America. When he continues to do this despite the Dem victory in 2006, it should take no Kossack by surprise.
But the second prong of his lameduck rule will be that he will frame Democratic critisms and attempts at oversight as excessive partisanship, both as cover for his imperial violation of seperation of powers Constitution principles and as a offensive means to paint the Dems as soft on terror, etc.
I think the best means to counter this will be to pass legislation and seize the political spotlight. Lets pass a minimum wage increase, stem cell measures, health care, etc. Lets force Bush to put his opposition to these policies in the public light and create a long list of examples of Bush's failed domestic policies out in the public light for people to see come 2008.
As for oversight and criticism, lets never back down from exercising Congressional oversight and upholding the Constitutional principles that the founding fathers envisioned when they created a legislative branch which was not a rubber stamp for the President.