How about a trans-Atlantic task swap? Simply have the Cardinals hammer out a deficit reduction deal and let the U.S. Congress select the next pope. Remove the political context in both cases, reason and compromise prevail and everybody's home in one day.
Republicans on Capitol Hill have dug themselves into a deep and narrow chasm whose walls are about to close in. In a matter of weeks, they may find themselves squeezed mercilessly between their implacable right wing and constituents feeling the pain of sequestration.