Take the $120 billion deficit for the 2013 budget as things now stand and give responsibility for one half of it to each party. Both the Senate and House could agree initially that they will accept and put together what is decided by each party.
Republicans do not want to increase revenue, so they would be tasked with increasing revenues $60 billion. They can do it by any means, as long as the Congressional Budget Office agrees that it will increase revenue by $60 billion.
Democrats are resisting cuts to benefits, entitlements and programs. They would be tasked with decreasing expenses $60 billion. They can do it by any means, as long as the CBO agrees that it will decrease expenses by $60 billion.
The wasted time, frustration, blaming and inertia are produced in quid pro quo arguments across the aisle. Separate tasks would leave each party to battle internally from supposedly similar perspectives, goals and values.
Each party would be given the area they wish to protect so they can modify it carefully. This process could be applied to the state budget in Olympia as well as the federal budget in D.C.