Hate it for numerous reasons:
For one, I think there is something to the idea that teams play worse on short rest. I don't need to see two exhausted teams playing on Thursday, I'd rather see two fully rested teams play on Sunday. I want players to stay healthy and be well-prepared so the best product is on the field.
It messes with fantasy stuff; now I have to check earlier in the week if I have any Thursday players going that need to get in my lineup, and maybe forces me to make lineup or waiver decisions earlier than I'd otherwise like to (e.g. if I have a questionable QB playing Sunday and his backup playing Thursday, I now have to decide Thursday night which one I want to start). It gives less time to get trades worked out before the fantasy week starts, etc. Mildly annoying.
But the main reason is it's just oversaturation. I've always thought that the great thing about football compared to all the other major American sports is that it's just one big day a week (with the exception of MNF, of course). I have a feeling there may be a strong East Coast/West Coast divide on this, but now it's three nights a week I'm up until midnight watching football, and all three nights I have work the next morning. I have other things I need to be doing, I can't waste all day Sunday AND three nights every week watching football, so I end up just not watching the Thursday games anyway. It was fun having football on Thanksgiving Day every year as a special Thursday event, but this every Thursday bull#### just takes away the novelty of it. We're only a couple weeks in and I'm sick of it already. Didn't watch a minute of the Rams-Cards game last night.
NFL: If it ain't broke, don't fix it.