Divided Government Theory of Policy Change
I think the Iraq surge may be an example of a policy that could possibly be more easily pursued under divided government:
Assume for a moment that both Democrats and Republicans want to pursue a counter-insurgency strategy as recommended heavily by Petraeus and Mattis (and heavily promoted by TPM Barnett). This strategy obviously has heavy political costs; consider point number one:
The more you protect your force, the less secure you areHowever, under divided government, it may be possible for both sides of the political spectrum to effectively share blame for these costs while giving up no relative advantage (i.e. since the costs are shared approxiamately equally, no relative loss is incurred).
Under the current trajectory of the policy it seems likely that the Republican executive is attempting get the legislature to sign off on this change in strategy (which in fact really requires no additional troops or legislative invlolvement beyond the status quo) by creating an artificial new circumstance which will require the legislature to make a new choice of exercise of its veto power. By failing to exercise this veto power the legislature could be portrayed as offering tacit support to the policy. It seems that the Republican executive will be successful in forcing this tacit approval since there will be a very public crisis costing Iraqi and possibly American lives (depending on the foolishness of the Republican executive and the responsiveness of the American Public to the deaths of Iraqis) which will only have a short term solution coming from tacit legislative approval of the new strategy.
This was not possible under the Republican unified government of 2005-2007 because it would require the political right to bear sole responsibility for the costs of the new policy.
The key is the abilities of either branch of government to precipitate a crisis that can only be solved by the (non) exercise of the veto power of the other branch. Normally the legislative branch has the upper hand in that it can set the agenda of national discussion by passing bills and sending them up to the white house. This is a case where the opposite is true.