Just had a chance to watch it again. Her voice is a little slurry but definitely not in a drunk way. She could just be a little nervous, as she hasn't done many TV interviews for a while and she's there on her own. I also noticed it in interviews she did here on the radio a couple of years ago.
I hope you all get to see the clip soon. It's worth it just for the studio footage - her and Lindsey look great together, and she does give him a very warm hug
edit...its' more of a stutter at one point rather than a slur, which makes me think it is just nerves