Unfortunately, it seems like the GOP doesn't know what to do about the fiscal cliff. They are in a cursed either way situation. Part of the reason is that the last presidential cycle was about little other than economics on the GOP side once the primaries were over. Columnist Pat Buchanan analyzed this here.
So what can the GOP do? Another columnist, Hugh Hewitt made a Defense proposal here which suggested that the GOP take the Defense budget out and pass it separately for at least a partial victory.
Let me know if you have any suggestions yourself, including just going over the fiscal cliff and then dealing with the consequences later.