Mix mic audio and system audio and simultaneously record using Audacity
I'd approach the problem from the opposite end...  

Get the YouTube audio track into Audacity first.  

You can use iTunes to extract audio from video  


In prefs > General, click Import Settings... &amp; change 'Import Using' to WAV [remember to set it back to your preferred audio format afterwards] 
Drag your video into iTunes, then go to the Movies tab  
Select the movie, then File menu > Create New version. Hold the  Alt ⌥  key &amp; the 3rd option will ungrey, allowing you to save the audio separately.
Import this to Audacity.


Then you have all day to record your vocal track separately; add reverb etc &amp; export the finished mix from Audacity.

This approach not only gives you the  time to go back &amp; edit mistakes etc in the vocal track, it also avoids the essential difficulty of trying to live-record 2 audio streams to separate tracks without professional audio equipment.