There is no “cliff” in the fiscal cliff because tomorrow, on a practical level, relatively little will change for many people if there is no deal. Even if tax rates technically go up on everyone, it is unlikely most people will change their actual tax withholding since they know a retroactive fix will come eventually. The most important thing that happens at midnight is that the baseline changes.
Today taxes are low but by tomorrow the Bush taxes cuts will have expired for everyone. Any deal reached today that only extends most of the Bush taxes cuts can be theoretically framed as a tax increase, since Congress would be voting for a tax rate higher than currently exists. By tomorrow, though, this entire issue goes away.
Starting tomorrow the only question will be how much to cut taxes relative to the new baseline. The question will no longer be “how many of the Bush tax cuts should be extended?” but “how large should the Obama tax cut be?”
While this is a seemingly stupid technicality, politics often turns on technicalities. Once we start using the new baseline it should be easier to get Republicans to vote for a deal, because no one can claim they are voting for a tax increase. Any Republicans still holding out will find it difficult to defend the position of opposing one of the largest tax cuts in American history simply because it doesn’t cut taxes enough for the super rich.