While I'm sure the Gamepad factored into the cost more so than an average controller, I'd also think the processor(s) probably ended up costing them a bunch. Despite the relatively lean amount of silicon, you've got 3 different companies (Renesas, AMD, IBM) and the licensing fees involved with that. IBM gave them a custom chip using an SOI process, which adds to cost. You had the Renesas eDRAM and all the costs and custom process node to go along with that. Also, the Xbox 360 is sitting at $199 even now. The last generation of consoles simply weren't able to be reduced in price as much as previous generations.
Let's say that Reggie meant the basic console when he was talking about having to sell a first party game along with the console to break even, that's still over $300 (taking into account a retailers cut) that they were looking to make back, I just don't see how WiiU could have possibly cost them that much to manufacture esp when they didn't even include basics like an Ethernet port... Even being conservative I would say the Gamepad cost them at least $100 to manufacture at launch and for much of 2013.
Didn't one of the guys from chipworks in the gaf thread estimate the main MCM to cost ~$100 ? If we are taking that as fact then I really don't believe that the WiiU's eDRAM, DDR3 RAM, WIFI chip, ARM CPU, pitiful storage, disk drive, tiny fan and case cost anywhere in the region of $170 to manufacture in late 2012 if you're going on the notion of a $30 to manufacture Gamepad for instance. It makes much more sense to estimate the main MCM to cost ~ $100, the other components combined to cost ~$100 and the Gamepad to cost ~$100 giving us the $300 Nintendo needed to break even (it could well have been closer to $350 they needed to break even if Reggie meant the Deluxe pack).
I also feel the MSRP of the console backs up the case for a $100 Gamepad. You could argue that they aren't cutting the cost of the console now because it's a lost cause but I think we would all agree that if Nintendo could have price cut WiiU to $249 or even $199 in late 2013 or mid to late 2014 you can bet they would have done it esp with the likes of 3D World, MK8 and Smash launching during those times. I believe they simply couldn't do it without incurring massive financial losses caused by the Gamepad's high manufacturing costs. The main MCM aswell as all the other components (outside of the eDRAM because of Sony's factory purchase) would have drastically dropped in manufacturing costs by that time aswell meaning they could have cut to $249 or $199 if the Gamepad really did only cost $30 to manufacture.
In hindsight they should have removed the Gamepad from the console, bundled a pro controller as standard and price dropped the console to $199 and completely re branded the console in time for MK8 launching, it wouldn't have turned the consoles fortunes around but it would have been sitting at closer to 20 million sales now instead of 10 million imho.
However powerful NX is I hope they follow Sony's lead of using cheap, standard off the shelf components that can be price dropped a couple of years into it's life because the sooner they hit the $199 - $149 mark the more appealing the console becomes to their main demographics - families, kids, core gamers as a second 'exclusives only' console. Releasing at $300 or more will see them again only appeal to the same hardcore Nintendo fans that bought WiiU.