The thought is that a country undergoing a debt crisis, if they have debt denominated in their own currency they can just increase the money supply and inflate their way out of the debt crisis. You can do similar to attempt to alleviate any balance of payments problem, by devaluing your own currency and therefore making your exports relatively cheaper and imports more expensive. When Greece when through their debt crisis they had no ability to change their monetary supply because its controlled by the ECB.
Its one of the oldest arguments in economics which goes back 100 years now (was being argued back in the 20s with Germany's post-WWI reparations, debt and resulting hyperinflation). Its more detailed than left v right, but to put it generically the left believes that developing countries should stay aware and keep their currency relatively undervalued to help with domestic industry and exports, whilst the right believes that you should let your relative currency value float freely, keep your govt accounts healthy and low capital constraints to allow you to attract more investments both into funding govt debt and also the private sector.