YouTube and GodTube videos aren't licensed for public presentation or consumption.
The YouTube terms of service clearly state this.
The full document can be found here, and the section on usage is as follows:
5. Your Use of Content
In addition to the general restrictions above, the following restrictions and conditions apply specifically to your use of Content.
The Content on the Service, and the trademarks, service marks and logos ("Marks") on the Service, are owned by or licensed to YouTube, subject to copyright and other intellectual property rights under the law.
Content is provided to you AS IS. You may access Content for your information and personal use solely as intended through the provided functionality of the Service and as permitted under these Terms of Service. You shall not download any Content unless you see a “download” or similar link displayed by YouTube on the Service for that Content. You shall not copy, reproduce, distribute, transmit, broadcast, display, sell, license, or otherwise exploit any Content for any other purposes without the prior written consent of YouTube or the respective licensors of the Content. YouTube and its licensors reserve all rights not expressly granted in and to the Service and the Content.
GodTube is also not intended for broadcasting.
We contacted GodTube about playing clips in fullscreen and here is their response:
The content you find on Godtube.com is intended for personal use, not for broadcasting or playing at public gatherings.
The videos you find on Godtube are intended to be shared with your friends and family through a number of different ways including: email, Facebook, Twitter, Stumbleupon, Digg, and a few others. We do not currently offer the feature to download or burn a video from the site. However, in the near future we hope to make this feature available for select ministries and partners.
CVLI Licensing does not license use of YouTube (or GodTube) videos through MediaShout, either.
CVLI licensing isn't designed for video clips but for movies (motion pictures).
1. Christian Video Licensing International (“CVLI”) grants licensee (“LICENSEE”) a non-exclusive license (“License”) to publicly perform copyrighted motion pictures and other programs from any legally obtained source intended for personal, private, home use only – such as DVDs, in its “Facility(ies)”, under the Terms and Conditions specified in the CVLI Agreement (“Agreement”).
In non-legalese:
"CVLI does NOT cover streaming video clips from Youtube or any other "non-purchased" media, unless that video clip is owned by the person who posted it to their website and you have permission to use it."
The good news:
You can purchase both worship videos and backgrounds from our Media Store that are designed and licensed for exactly what you're wanting to do. :) Be sure to check out our Subscription Plans to save on your purchases.
If you are the author of the video or have permission from the author to use it, edit the URL after you insert it into a Web cue so that it looks like the following. This will play the video full screen. Please understand, YouTube is taking steps to prevent the use of their content in a public setting, so this may not always work.
Please note "_popup" in between "watch" and "?".
https://www.youtube.com/watch?v=QweT9QJaGcc&list=PLXQ0Ok4FZvgcN8RbR1ZTGrY52OsklYhY_
https://www.youtube.com/watch_popup?v=QweT9QJaGcc&list=PLXQ0Ok4FZvgcN8RbR1ZTGrY52OsklYhY_