1080p60 depends on the developers, not the hardware. Few HD games run on 60 FPS while Nintendo almost always delivers 60 even though the Wii is much weaker than the HD systems. Developers have to decide how to allocate the system's resources and if they decide to spend the power on making it pretty instead of making it fast then the resolution and framerate are going to suffer no matter what the hardware does.
I think Nintendo will likely make games run at 1080p at a steady 60 frames per second. That's just how Nintendo operates.
Of course you are right that developers make choices about the resolution and framerate that their games run in, but let's not overly downplay the importance of hardware in how these outcomes are reached. Hardware specs define the set of trade-offs that developers face when crafting a game's visuals, and therefore establish the set of options that developers have to choose from before they apply their preferences and priorities to the problem and reach a balance that they think fits their game design best.
For instance, it was possible to achieve 60fps even on N64 (as demonstrated by F-Zero X), but the sacrifices necessary to achieve this in terms of detail, draw distance, polygon count etc. were so severe that it would not have been really viable for Nintendo to try and make, for example, a Zelda game that ran in 60fps on N64. I'm sure it wasn't literally impossible, but in practice the hardware limitations of the N64 essentially prevented this from happening, not just Nintendo's discretion.
Of course, today's consoles (and tomorrow's in the case of Project Cafe) don't present constraints nearly as severe as the N64, but they are not yet so powerful that fundamentally similar trade-offs have ceased to exist, and so again certain kinds of games are less likely to run in 60fps and/or 1080p than others. Nintendo develops and publishes a very wide range of games, so I don't expect to see a one-size-fits-all policy from them.
In many cases I think framerate will be a priority: responsiveness-leveraged games like Mario, Punch-Out!! or F-Zero are very likely to run at 60fps on the new console, and if it's significantly easier to do that at sub-1080p resolution, then chances are Nintendo will make that trade-off. On the other hand, a game like Pikmin with its unique, highly-detailed visual style would likely benefit more from 1080p support than a silky smooth framerate, and again--dependent on the hardware specs--it may be not be possible to have both without compromising Pikmin's aesthetic in some way, which Nintendo probably would not think is a worthwhile sacrifice just for a better framerate in a game of its kind.
I do think though that Nintendo tends to prioritise functionality and is clearly far less concerned with making games that look gaudy in screenshots and online videos than most HD developers have been, so it wouldn't surprise me if we saw more 1080p/60fps games from them than anyone else, I just don't expect it to be nearly enough of a priority for them to see it happen across the board or even the majority of the time--they will tailor the visuals to the needs of each individual game according to the possibilities set out by the hardware, creating a whole spectrum of different results.