Does this only happen for one particular slideshow? Test by creating another, short slideshow using different photos. Can you export this test slideshow? If yes, then probably one of your photos cannot be processed. Duplicate your slideshow and try to find the problematic photo by removing photos from the slideshow and trying again.
If you cannot export any slide at all, create a new iPhoto library for testing. Use iPhoto's "File" menu to create a new library: File > Switch to library > Other/New. Import a few photos and try to export a Slideshow. If exporting from a new library works, try to repair or rebuild your regular iPhoto library.
You rebuild the library by launching either iPhoto while holding down the key combination⌥⌘ (option-command) and double-clicking the iPhoto icon. Keep holding down the keys, until you are seeing the Library First Aid panel. Select to "Repair" the database.
If that does not suffice, try "Rebuild".
Back up your library before rebuilding.