I can understand why some Swiss would feel sensitive about English speakers moving into their country and not trying to learn the native language. Some people in my country freak out whenever they see signs posted in English and Spanish. From the Swiss point of view, English is Spanish. That's part of the reason why I haven't joined in the chorus of "Rule Brittania." While you're in Switzerland---and I realize you don't have time for lessons---learning to say a few polite phrases in German or French might help grease the skids. "Please", "sorry", and "thank you" can go a long way.
One more thing---Teverus DOES have a good point. While I can provide EFers with an insight as to how things are in America, the other posters who actually live (and some of which were born) in CH can give you more practical advice about living and working in Switzerland than I can. If you don't burn your bridges, this forum can be a lot of help.