Nintendo doesn't even necessarily need to make an FPS, though that would be nice. One of the biggest missed opportunities for me on the Wii was that Nintendo never made or published a 3rd person shooter, a genre where I thought the Wiimote's pointer functionality really shined in titles like Resident Evil 4. They did publish Sin & Punishment 2, but while that was good (and I really should finish it one of these days) it really wasn't the same sort of experience as something like an Uncharted; Dead Space; or Resident Evil. I suppose Battalion Wars could have been that, but that seemed to get dropped fairly quickly. A Nintendo-exclusive FPS would be nice, though.
Sony's certainly made more than its fair share of mistakes this generation, but I think as far as software lineup is concerned they have the best variety of experiences on the market. Unfortunately, as Shane Satterfield was saying on GameTrailers' Invisible Walls and Bonus Round shows a few weeks back, they have all these interesting and quality experiences. However, the vast majority (if not all) of them have not sold to expectations (especially FPS franchises like Killzone and Resistance) and at this point I don't know what more Sony could do to change that.