Use the search function - type in "American", "work permit", "visa", "dependent" etc....there's a whole lot of answers on here and a few options for you. Main one its - it's near impossible

You could apply for a job (do you speak German), you could become a student and apply for a student visa (gives you more time).
If you have job qualifications needed in Switzerland you're in with the best shot, otherwise it's hard. Use the search button and you'll find a lot of cases like this. All responses from 2008 are still pretty valid. You could call the Swiss embassy in America and ask them if there are any options from there (Long term visa) maybe after you find some options on this site.
Good luck.
Luzern is beautiful.