Even with only about two percent of American exports going to Europe, a severe recession in the region would affect the US beyond the direct effect on exports.
Paul Krugman notes that only about 2% of America's GDP consists of goods exports to Europe and argues that even after increasing that number by 25% (to 2.5% of GDP) to take service exports into account that means that there is little reason to expect a downturn in the European economy to affect the U.S. economy.
But first of all, while no country or region specific data for service exports exists, total service exports is more like 40% of goods exports as goods exports was $126.6 billion while service exports was $51.3 billion. America's exports consists of services to a much higher extent than most other countries (with some exceptions like Britain and Hong Kong).
Still, with a 2.8% of GDP estimate for total exports, even a 25% decline in exports would at most reduce GDP by only 0.7%, less to the extent that the value of exported goods consists of imported input goods.
However, while America because of its size is less sensitive to developments in Europe, and other parts of the world, than most other countries, a severe recession in Europe would affect it beyond the direct effect on exports to Europe for two reasons.
One is that because other countries in the world also export to Europe, their economies will weaken too, weakening U.S. exports to those countries as well.
The second, and more important is the effect that globalized financial markets create. When there is panic in one market, other markets usually panic as well. Europe experienced that in 2008 after the Lehman meltdown. And if there is a similar meltdown now in Europe, America will experience it too.