Not sure how you want to handle this, for know I have hardcoded it in the plugin.
You tube videos require you to pass "wmode=transparent" at the end of your iframe src attribute to prevent the video from appearing on top of other Items (like menus on the page).
I have modified the plugin code to read:
<iframe src="http://www.youtube.com/embed/'.$video_id .'?rel='.$rel_param.'&wmode=transparent" frameborder="0" allowfullscreen></iframe>
It may be more appropriate if you update the plugin to be able to pass the wmode in as an param in the shortcode:
[responsive_youtube NbCr0UyoFJA norel wmodetrans]
Thanks for the simple straightforward implementation.