The world today has an economy that is very highly interconnected as a result of globalization. Therefore, stress in one country (so long as it is a major country) can put great stress on other countries as well. This means that Obama's efforts to fix the US economy have, to the extent that they have been successful, helped Europe as well.
The United States is still the world's largest economy. As such, it is a major trading partner for many other countries in the world. Financial stress in the US decreases US demand for products from other countries. This is bad for Europe as well as for other regions of the world. The US dollar is also the major reserve currency in the world. Stress in the US economy hurts the value of the dollar and, thereby, Europe's reserves of dollars.
The interconnectedness of the world economy means that financial difficulties in a country as big as the US will lead to problems in other countries. By easing problems in the US, Obama's efforts help other countries such as the countries of Europe as well.