I mentioned one quickie way to make an on-the-spot-background here, so I thought I'd mention another fast way to produce unique backgrounds when you're limited by time and/or options.
1. Grab a still image or a freeze frame (Shift + N) from your footage. Pick something with colors that match the project you're cutting or at least fit the mood.
2. Dump it into the Timeline and add Gaussian Blur. Video Filters > Blur. Really just about any type of massive blur will work here. The key is to blur it by a huge amount.
3. Scale up the blurred image by a bunch, 300% or more even.
4. Keyframe it so it slowly rotates, or slides left or right or moves up or down, up to you. Slow adds the feel of it being animated when it's not. Experiment with different speeds and/or different areas of the image; you'll be surprised how animated it can end up looking.
It can work particularly well beneath some generic text or title cards. It may not be the prettiest but when the clock is ticking…