The process is somewhat involved but it can be done.
The Short Barreled Rifle is govern by the National Firearms Act, commonly referred to as "NFA".
You have to basically do one of two things, register a full SBR rifle under a Form 4 or register a lower receiver under a Form 1. The difference is whether you want to purchase one (Form 4) or build one (Form 1). Here are some links:
http://www.atf.gov/firearms/faq/national-firearms-act-short-barreled-rifles-shotguns.html
Want a Short Barreled Rifle? Here's How | The Truth About Guns
The wait time will be the hardest (think 9-11 months), once you have found a rifle or begin the process of registering a lower receiver. I would recommend talking to a lawyer regarding the use of a trust. I had a lawyer here in Nevada set up a trust for me for $200 and it is great. Without a trust, you must be present during the use of the SBR at all times. You cannot loan it to anyone, not even a family member. With a trust, you simply add someone to the trust and they can use the SBR. The use of trusts and their requirement for local law enforcement sign off, photos and fingerprints is currently in limbo, but if I had to guess, you could start the process now, prior to the possible rule change, and then hope that they do not go retroactive on already submitted applications.
The other problem is traveling with an SBR. You must get permission from the ATF prior to crossing state lines. See the FAQ from ATF regarding NFA items:
http://www.atf.gov/firearms/faq/national-firearms-act-firearms.html#lawful-transportation
I just recently went through the process and I am glad to have a rifle that is so easy to maneuver with, especially for my 3-Gun competitions. If you have any further questions, just private message me.
Good luck and let us know what eventually happened.