This can be achieved by following instructions for placing a background video on a website using HTML5. This article should get you on your way: http://demosthenes.info/blog/777/Create-Fullscreen-HTML5-Page-Background-Video
You would just use one of the mp4 files that are associated with your video. Depending on the download connection of your viewers and the quality you want to serve, you may want to choose a lower encoding profile (360p or 480p). You can find the link to these files via Edit > Manage for a video.
Use "autoplay" and "loop" in the
<video> tag to display those functions.
Here's an example of what the embed code would look like:
<video autoplay loop poster="bgvideo.jpg" id="bgvid">
<source src="polina.webm" type="video/webm">
<source src="http://www.viddler.com/file/d/d02d7349.mp4?vfid=7781075a4122d7d8669df493e378ff60" type="video/mp4">
Note: Replacing a video will renew the video URL, so you will need to copy the link again and paste it into your code.