Political parties are less supportive of wars started by the other side's Presidents.
This is one of the reasons why I think it is going to be a big deal. None of the GOPers will want to take the position that the Obama policy towards the Islamic State is the right policy, which means they will have to propose something different - and specific. That means talking about sending in troops and expanding the bombing, or on the other side stopping the bombing and trying to focus on diplomacy.
It will also be interesting to see where Hillary stands on this. She has been critical of Obama on not dealing with ISIS earlier. By this time next year she will have her own policy prescription. And whatever that is, the GOPers will want to contrast themselves with that. If Hillary is mostly unopposed for a Dem primary, she may even be calling for more aggressive action (noting the humanitarian angle to stopping ISIS).
So GOPers would have to find a position that is differant than Obama and Hillary. While Obama has been the obsession of the GOP, by this time next year they will begin the transition to going after Hillary more.