They believe that even though they lost the presidential election they can still act like they won, and can ignore the wishes of the American public. If Obama and the democrats wish to finally convince the American public that they are not just pushovers, they can't give in to the republicans and just cut spending without increasing taxes, even if it means going over the fiscal cliff.
It appears, though, that the republicans might be willing to compromise, which is a step in the right direction because we can't just have tax increases or just spending cuts. Neither is enough to reduce the deficit. What we have to do is make the tax rate for the wealthy the same as it is for the middle class, and we also have to cut unnecessary spending.