Do have to have special rights to make a music video of a cover song, or can you simply pay the same mechanical royalty rate you would simply doing a cover?
You need special sync rights, which needs permission and special fees from the publisher. Expensive.
In short : don't do it, unless you're going to do it like the rest of YouTube generation and just do it for free and upload it to YouTube for the exposure, with the full expectation it'll be removed at the request of the copyright owner for being illegal some day.