I've only noticed this with a couple of games, but I'd love to hear if anyone else is having this problem.
I should start by saying that I own VC games on my Wii, and while input lag is present (as there is on all of our LCD and plasma TVs), it's bearable. I've beaten SMB: Lost Levels, Castlevania, Mega Man 3, and other difficult games on the service.
Last night, on a whim, I purchased Super Mario Bros. 2 on the Wii U eShop. When I fired the game up, however, things did not feel right. I'm not trying to boast, but I'm very well versed in this game. I know exactly what it's supposed to feel like, and I know what it should feel like with some minor input lag introduced by a flat screen TV.
This, however, did not feel right at all. It is almost like there is an extra frame or two of input lag on top of what I'm used to experiencing. I was having so many deaths in the game from overshooting my jumps, which never happens. I've owned this game on the NES, the GBA, and the SNES (All-Stars), and I know this game like the back of my hand. What I was experiencing last night was not normal.
So, I thought that maybe the lag was being introduced from my receiver (despite not feeling any substantial lag before). I connected the Wii U to my TV directly through HDMI. If the lag was any better, it was hard to notice. I also tried plugging it in via component cables, but STILL, the game just didn't feel as responsive as it should.
I think this is what was also bothering me about Kirby's Adventure (a game I'm less familiar with). I originally thought the game was just very sluggish because it was a late NES game, but I think I'm seeing now that there may be some input lag on top of all of that.
Is anyone else experiencing this? I found people on Reddit who were equally upset. Nintendo, please patch these games so that they don't feel so unresponsive!
Edit: I should also note that people on Reddit were saying that even games in the Wii U's Wii Mode felt more responsive than some of the games from the Wii U eShop.