I'm not sure how to define pickiness... I have never shot low-resolution full frame, and actually have very little experience with cameras of exactly 12 mp. I have experience with cameras in the 4-10 mp range, but jumped from 10 to 16. I've looked at images from other people's 12 mp cameras, but never owned one, so my answer is likely to be unsatisfying..
That said, here's my best supposition. I have never seen a camera with less than 12 mp that I'd be comfortable with as large as 16x24, which is the largest easy size from a 17" printer. Both 16 mp from the very old (but very high end for its time) Canon 1Ds II and 16 mp from the newer Micro 43 cameras are borderline, depending on how much detail is in the scene (they work for many, but not all subjects). I'd imagine the D700, which has less resolution, but a reputation for an extraordinarily good sensor for its time, is probably in the same category. Most other 12 mp cameras (other than the new Sonys) are probably a small category below the D700 - good up to 12x18", really pushing it any bigger.
One possible rule of thumb (it works for me, with the cameras I've tried it on, but I'd want more evidence before saying I was anywhere close to sure) is that the resolution in megapixels roughly equals the short edge of the largest comfortable print? Subtract one size for a small or poor sensor (only half a size for a semi-small sensor like micro 43), and perhaps add a size for an extraordinary sensor, or one that is unusually large for its resolution? This passes the sniff test on a lot of cameras I am familiar with:
8 mp iPhone: 5x7 (subtract one size for a small sensor)
10 mp Nikon D200: 10x15 (this matches my memory)
16 mp Micro 43: 12x16/16x20 (subtract half a size)
16 mp Fuji: 16x24 (done this a lot, and it works well)
24 mp Sony sensor (any modern one): 24x36 ( the only camera with such a sensor where I would say "not quite" is the original NEX-7, and that may have partially been less than great lenses).
36 mp+: enough bigger than my printer that I've never found the limit with any confidence.
EDIT: On further reflection, I realized that the one group of cameras this understates the performance of is very early DSLRs - A Nikon D1 or Canon D30 were capable of more than 3x5 (although 3 MP compacts really weren't). Similarly, a 6 MP DSLR easily outperforms an 8 MP iPhone, and can go somewhat higher than 6x9.
There's also a point at the very high end of the range (whether this is 24 mp, 36 mp or even higher in what is presently medium format territory is debatable) where viewing distance means that print size becomes effectively unlimited. Sure, you could use more resolution if you stuck your nose up to the print, but how close are you going to get to a 40x60" print, much less a 100x150" print? A practical limit is that the best (highest resolution and best color quality) printers are rare above 44" widths, and simply do not exist above 60". The grand format printers that are the only way to print many feet wide are made for signage, and just don't have the image quality of the Epsons and Canons that dominate the 17-44" market. They also don't print on the baryta and art rag papers that the 17-44" machines do.