This is a complex issue (central banks use models with 2,000+ variables to simulate this), and it's off-topic so I don't want to elaborate much.
You simply didn't think around enough edges. A goods trade balance deficit equals a capital transfer deficit and lower prices broaden the base of customers. Finally, production can be changed to different goods to meet demand elsewhere.
Guess what? The American trade balance deficit isn't being paid for by Americans. If the Americans suddenly stopped buying, they would also stop lending. The money would stay outside, the goods would stay outside - and people would simply buy more stuff with their own money after a short (2 years at most) phase of adaption.
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Some statistics that show the moderate relevance of the USA for Europe:
Germany (a country with extreme trade emphasis) has only 7.5% of its export trade (about USD 100 billion) and 4.5% of its import trade (about USD 49 billion) with the U.S..
A total embargo of the USA would only cause a dent (about a quarter) in the German trade balance surplus.
(Let's keep the calculations simple like this; this is not a doctor's thesis, after all.)
EU as a whole: 23.3% (USD 310 billion) / 13.8%. (USD 202 billion) - intra-EU trade excluded.
The difference is about USD 108 billion - less than a per cent of EU GNP and even the exports are less than 2 % of the EU GNP.
The perception of extreme interdependence comes solely from the financial markets, which have illusions as their business model. The real trade & hardware interdependence is marginal - most U.S. products have perfect or close substitutes in the EU.
Most of these were 2005/06/07 figures, CIA World Factbook.
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