I use a Debian testing distribution (x64) and the hangouts complement just didn't want to work (in firefox), always asking for its installation when trying to have a video "hangout", even though it's installed. Turns out that there is a particular library that prevents the complement from working, and that is libudev0.
Ironically, this library is no longer in the Debian testing repositories, using the more recent libudev1 instead. In order to get the complement to work, these steps should be enough.
Make sure that libudev1 is installed (which probably is):
$ dpkg -l libudev1 ||/ Name Version Architecture Description +++-==============-============-============-================================= ii libudev1:amd64 204-6 amd64 libudev shared library
Purge the complement (if installed) and remove the libudev0 library:
# apt-get purge google-talkplugin && apt-get remove libudev0
And then install the complement again. In my case:
# dpkg -i google-talkplugin_current_amd64.deb
Now, after restarting the web browser, the complement should work correctly.