Perhaps the best way forward for the GOP addressing the "fiscal cliff" is to play small ball and just pass bills patching specific items. One bill that extends the expansion of the family tax credit, one that preserves the 10% tax bracket, one that extends the payroll tax cut, and also bills extending the capital gains and dividend tax cuts. Clean bills that don't do anything else.
Once these individual bills passed the House, the ball is in the Dems' court as to which tax cuts they want to keep. If they want to extend a specific cut, they can do so easily by passing it through the Senate and signing it into law. If Obama doesn't like the "tax cuts for the rich," the Senate can easily kill the capital gains and dividend cuts that predominately affect higher income taxpayers while extending the cuts that don't. But the sequester happens as scheduled, the other spending doesn't get extended, no new spending is enacted, and Obama has to bargain separately for the debt limit increase..