Passet behöver bara vara giltigt under tiden man skall befinna sig i USA.
http://sweden.usembassy.gov/consulate/faqpassports.html
Does my Swedish passport have to be valid for six months?
Your passport must be valid on entry into the U.S. If the passport is not valid for the duration of your stay, you will be required to apply for a new passport from your Embassy while in the U.S. If your visit will be of short duration during which time your passport will expire, we recommend that you obtain a new passport before traveling as you will be admitted only until the date on which the passport expires. Such action before you depart for the U.S. will save you the inconvenience of applying not only for a new passport, but also an extension of stay.