I lived in Brussels (with a US passport) for about a year, though it was just before 9/11. Brussels airport is not especially large and they processed people fairly efficiently. As the EU parliament and NATO are headquartered there, it does get a decent amont of fast in and out traffic. Even living there, it was not uncommon for me to pop in for less than 24 hours and then be gone again. I never had any problems with passport control at the airport. Personally, I doubt there will be any problem.