The Democrats propose taxes on the wealthy to balance the cuts, the Republicans oppose that because there is nothing worse for them than taxes on the wealthy. The Republicans sort of propose various cuts (sort of since they do not have a unified proposal) or maybe propose extending other tax cuts (and how does that pay for cuts?)
Given that the deadline (at least the deadline for anything that starts January 1, 2012) is approaching there will be a continued flurry of discussion, and maybe activity. I expect one of two results: no extension (but maybe something in early 2012) or a very messy extension (with many additional items — not just a simple targeted tax increase).
Politically, the President can profit from no extension (something to attack the Congressional Republicans with for the next (election) year) or a clean extension. Something messy does not help because any impact will be lost in the clutter.
Economically the impact is more difficult to measure. Any cut in income hurts a portion of economic activity. But the payroll tax does not impact everyone so the impact may be less than predicted. No one is talking about the great benefits of the current cut. Tax cuts tend to be more like interest rate cuts: they have a very short term impact, then it is back to normal.