The Instability of Monetary Union
Fiscal and political union is necessary to the survival of monetary union, assuming that the united economies display heterogenous responses to real and nominal shocks.
Assuming a basic model of monetary policy in which the central bank can target a nominal aggregate across the monetary union, it follows that for the non-targeted nations or those "lost in the mix," there will be some nations for which monetary policy is overly accommodative or overly contractionary.
As the overly-accommodated nations experience inflationary demand growth, and the overly-contracted nations experience nominal recessions, the monetary policy has "passively loosened" or "passively tightened" relative to the monetary policy's goals, implied by the aggregate target. Therefore the countries individual nominal economies "veer off" in different directions as passive monetary policy exacerbates their heterogenous conditions.
The only way to stop this process is fiscal transfers or monetary breakup. If the overly-accommodated nations transfered some of their nominal income to the overly-contracted nations, that would close the gap and eliminate the passive tightening or loosening problem.
This is fundamentally what is happening in the Eurozone -- it explains the cause of the "fraying," or increasing variance, I observed in another post among individual European nations from mean Eurozone real output growth.
Update: Timothy Lee observed that labor mobility could help resolve the real dislocations; however, other factors of production, particularly fixed investment, are not mobile. This implies that monetary unions will still face the magnifying problem of passive loosening or tightening, given that long-run potential output cannot fully adjust to aggregate demand. Consider the example of German reunification: East Germany, even if the East Germans could have all taken up jobs in West German firms and left their communities, would have been left with even more unused capacity and would have become increasingly depressed without extensive fiscal transfers from the German state.