the right to privacy is only present in the US constitution as an interpretation of a "penumbral" right, that is to say a hidden intention from the authors. Other constitutions have it clearly written like the French or the British.
http://en.wikipedia.org/wiki/Privacybut the problem is mostly the relation between the American people and their government. The American government's interference with citizens life is in general (except for the actual breaches) very little compared to European governments. At the same time most Europeans don't feel that their privacy is violated, because they feel that they have delegated a part of their rights to the government to ensure that society protects them. Any European governmental form would be considered as ten times more "big brother" than the American one under normal circumstances. Americans have very little social rights compared to Europeans. Social rights need a certain invasion of privacy to ensure equity and prevent fraud.
The problem is not really the "spying in the bedroom". The problem is how to organize a relation of trust between the people and their representatives and induce mechanisms that prevent governments to misuse this trust. And privacy doesn't have to be the starting point "of the values we hold dear". Common interest and other rights (equity, welfare) can be the starting point. For example the European abortion rights are motivated from mostly a point of view of health and social rights and only partly from the right to privacy.