Shannon, I could be wrong here, but what you described sounds like a sampler issue to me, not really a looping one! But Skilz and Guess have given excellent pointers if you want to go that route. The same type of effect can be accomplished with a sampler (using the PS2 would be perfect!!). When you described the stutter effect with Tweet's song, the part or phrase that you want to stutter can be stored into the sampler. Then you can recall that sample as the song is playing to also produce the stutter (on beat increments, of course!), without having to loop the playing record. This is a cool technique and you might find it a bit easier to perform.
Then again, maybe what I'm describing isn't what you're looking for at all!! I just thought I'd throw it out there!!