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The EU gained serious traction through the late 2000s as the Lisbon Treaty was ratified and the EU's executive and legislative branches became significantly more powerful bodies than they previously were (as I've mentioned before, they begin to rival the powers of the former Articles of Confederation).
But as we know, a unified European continent is verging on the single greatest threat to the US' security. Obviously, the US is relatively preoccupied in the Middle East, but it is not this preoccupation that has kept the US from pressing on the EU (certainly the US is pressing on China and Russia).
Ultimately, the EU is a mixed blessing for the United States. There are some downsides--with a "united" foreign policy representative, it will be "easier" to stand up to the United States on foreign policy matters as a group with collective bargaining power (think of a trade/labor union). The EU could, as a group, threaten all sorts of nasty stuff as a whole, including pulling out of Afghanistan, or otherwise not supporting a US policy, that each state on its own would not be able to credibly do. But these downsides are mitigated by the very things that caused me to use sneer quotes earlier; the EU is not actually a terribly unified place, and probably won't be for a long time, if ever (in the US, it took over 100 years for states to shed their strong unique identities). Most EU countries have a very strong unique identity that the United States lacked when they came together, and already there is a fair amount of discord within the ranks. Italy is up in arms about an EU Court ruling over crucifixes in its schools. The UK is now majority in favor of full withdrawal from the EU (in order to protect its own sovereignty). With the Tories bound to be elected by March, this may end up happening--and if it does, countries like Poland and the Czech Republic may follow.
In general, a fair chunk of EU countries would rather not give up their sovereignty and independence to the extent that the Lisbon Treaty asks them to do, even for the economic benefits entailed by the Eurozone. But in general, the idea that many countries with such disparate geopolitical interests could get along is tough to imagine. The US has the dual advantage of coasts on its east/west, and relative weakness to its north/south (a number of wars have made that the case). Unity is geopolitically sensible for the US, but the EU has very different needs on its West (where it sees relative security) and its east (where Russia looms and the Balkans remain a hotspot). Western and eastern European geopolitical interests and needs will clash in the future as Russia tests the EU, and it may fall apart as the east forms its own alliance bloc with the US and UK (NATO largely faces the same risk as western Europe decides it would rather not suffer through standing up to the Russians again).
Ultimately, the EU will remain geopolitically fractured and weak. The bureaucracy of getting anything all done in the EU is horrendous, especially so for such a new institution. The EU will remain facing inward, trying to find a hopeless balance that works for everyone, instead of looking outward to challenge the US or even Russia. It will, at least, have a strong internal trade, which will ultimately be good for the US--a richer EU will mean not only more high quality products, but a bigger market to which the US can eventually export.
The EU will be an irritation in America's side for a bit as the US and EU diverge on geopolitical topics ranging from the Middle East to Russia to global warming, but the EU's very structure largely prevents it or any other European power from becoming a major geopolitical threat to the US, something with which the US should ultimately be quite pleased.