How can I get Nike+ to play songs from Spotify?
I'm afraid there isn't a solution currently available for this.  I've been using Nike+ alongside Spotify for over a year now by starting my Spotify playlist then starting a run in Nike+ and selecting "no music". I used to use iTunes playlists which worked with the power song feature and while that was kinda cool it's really not something I miss.

You might email them through their support page (couldn't find a feedback form) and mention it as a feature for future revisions.

http://nikeplus.nike.com/plus/support/#contact