Journalists with not much to write should note that this hypothetical is firmly on pig flying territory. There is an anglosaxon assumption that the Euro and the EU are unecessary so the breaking of the euro is a matter of time back to the natural order of things... Additionally talking to british politicians one gets the impression that deep down they think that it was all a matter of a Helmut Kohl & Miterran love-in in the 1980s and that the future is bright for tiny countries with mercantilist policies. This thinking is ofcourse deluded and a product of lazy economic nationalism, self interest disguised as idealism, breathtaking arrogance, and a short termism that diplomatically has led Britain to now have the smallest influence in europe in its entire history. As the small print says in all that rubbish investment products sold in UK banks "past performance does not guarantee future returns". The world where the UK could exploit vast swathes of the world because of the primitiveness of the natives are over. The world is now more sophisticated and massive trading blocks are emerging, and you better be part of one of them. Slovakia's establishment has understood that and is integrating into the most viable scheme possible to address the globalising challenge. To put it in other words, even if the euro were to fail, it would be replaced by a successor!
Things would have to get massively worse for the euro to be a liability rather than an advantage for Slovakia.
For this small country this border/labour/monetary (and in the future possibly even fiscal) union with Germany is of strategic importance, as it is for other small fiscally conservative nations dotted around germany, such as the Netherlands, Denmark, Finland, Czech republic, and not least Austria. All these nations share common values and high Human Development Index as well as raw GDP performance.
Additionally under the EU, schengen, and euro umbrella, Slovakia has redressed the economic isolation that came about from the iron curtain and the nationalisms of the 30s and 40s. Membership of this Neo-Austrohungarian economic zone, Czechs, Austrians etc is powering the economy and integrating it in big infrastructure investments that will further entrench these ancient economic links.
Economic integration under the euro is not an ideology or due to romantic visions of internationalism, but because globalisation is making this a necessity. If there are countries that at some point reintroduce currencies, they will have lost in the challenge of the emerging competitors (China, India) and will face a deflationary path to irrelevance and further nationalism. One has to only look at states with independent currencies and with no european perspective. It reads like a list of basket-cases in europe that are going nowhere (Moldova, Serbia, Montenegro, Albania, Ukraine) So the answer to the article is probably that Slovakia would probably the least likely state to leave the Euro.
The real question also is why so much focus on the euro and so little attention is paid to the printing presses of the dollar?? That is far more newsworthy..