A continuing frustration many of us have with the conversation taking place in Europe is that German and ECB officials continue to insist on viewing the problem of pre-crisis policy as primarily one of budget discipline when it was clearly one of trade and capital flows. A 2010 IMF working paper "Current Account Imbalances in the Southern Euro Area" (PDF) makes the story quite clear. Capital flowed from Northern European savers to Southern European borrowers. Those capital flows increased economic activity and nominal wages in Southern Europe. But as they show, relatively little of that capital went to finance productivity enhancing investments in factories and other production goods. Instead it mostly went to fund construction. Then when the construction boom ended, Southern European countries were left with wage levels that were out of whack with productivity. But was this a question of public sector borrowing? In some countries there was public sector borrowing, but on the whole this wasn't the issue.
If you run the tape backwards and then replay the entire Euro story with every Southern European government doing less borrowing, you'd still get the same basic story.
Now what is true is that public sector deficits contribute to current account deficits, so a rigorous program of deficit reduction should reduce overall current account deficits. But how much? A different 2010 IMF working paper on "Fiscal Policy and the Current Account" found through regression analysis that "on average, a a strengthening in the fiscal balance by 1 percentage point of GDP is associated with a current improvement of 0.2-0.3 percentage points of GDP." In other words, it helps but only a little.