Haha, I'm good friends with some die hard Chitown friends, lol. No, I've never heard of a unit that can do that.
Easiest way is to run a shotgun component connection to the TV, simply flip the input when you want it. Run audio too in case you ever want to have it at a lower volume with music, or in case of emergency raise up the volume when they actually kicked to Hester who is going for 110 yds. Component typically looks just as good as HDMI, sometimes it doesn't, other times it's better, just compare. Also, you can hook up an antenna, and if you get a signal, it will be even better than the cable box. (FOX and CBS show a lot of NFL.)
If the TV is up on a wall and it's too hard to run more wire, perhaps an HDMI splitter, however I admit I'm afraid the signal could die at the switcher, most particularly with STBs. I think there could be compatibility issues with HDMI in this particular scenario. I guess read up on some reviews, buy one that you can return easily.
Oh, agarwalro's experience is the first time I've come across something like that . . . of course it's still more expensive this way.