To flesh that out a bit ... place two copies of the video on the timeline, one above the other on two tracks. Add a blur effect to the lower clip. Use the cookie cutter to cut a hole in the upper clip. You'll see the blurred version through that hole. Place the cookie cutter over the face and use keyframes to move it around following the person's movement.

It's very easy to set keyframes on a moving face.

Make the size of your cookie cutter larger than the face to give you a little leeway.
Place a keyframe at the beginning of the clip so that it covers the face.
Go straight to the end of the clip and move the keyframe appropriately.
Now go to the middle of the clip and move the key frame again.

Let the clip play. You will now have an approximation of the keyframes you need.
Wherever the face isn't covered, you just keep doing the above, where you set a keyframe in the middle of two others. This allows you to very quickly have a pretty good outline of the keyframing needed. Then you can do your fine tuning.
Let the clip loop and watch it. Whenever the subject moves past the effect, hit pause and adjust your keyframe. If you are setting a lot of keyframes, you should zoom in on the timeline, so the keyframes are not all bunched together.

That covers the movement of blurrred mask. If your subject moves towards the camera or away, you may need to tweak the size of the mask as well.

It's an effect that is easy to do and looks professional.

I understand the instructions here for bluring out a face using the cookie cutter. I can get it to work great for 1 face. How can I blur 2 or 3 faces in the same still photo?

Naturally I am up against a deadline here so any help I can get would be greatly appreciated. Thanks

Chris