There is wifi in the parks now, so that may be an option for you.
Also, I don't think any of the resort lounges are going to have NFL Sunday ticket. So unless it's a national broadcast game, and the local teams aren't playing at the same time, your only option is likely ESPN zone. A couple years ago added a day upfront to my trip so I could watch the Patriots play San Diego in the Top of the World lounge. It was the biggest game of the week, and nationally broadcast. Unfortunately Miami was playing at the same time, in a meaningless game against another bad team... They were shown on the local broadcast instead of the Pats game... I was very disappointed, but learned a lesson to check for Florida teams playing the same time as the Pats in the future ;-)