This is an important question for the sasquatch researchers, of course, but it applies to many other areas of cryptozoology. In 2012, how well can big land animals evade us? (Note I specified land animals: I'm quite certain at least a few large marine species are out there.)
The best data to start with is of course recent discoveries of big land animals. If we start about 20 years ago, we have the parade of new animals from Vu Quang, a couple of which are still known only as partial specimens (the slow-running deer and the black deer). The Vu Quang ox is, I think, the last new full species to be accepted that can exceed 100kg. (Van Roosmalen's giant peccary from Brazil averages maybe half the size of the 100kg standard, but it's still important to note as a distinctive and pretty big new animal.)
There are, however, several cases of large populations of known species, some of them distinctive, and these certainly count in trying to assess what new species could still be hiding. We have the giant sable antelope of Angola: the odd-looking Asian elephants of the Bardia Royal National Park in Nepal: the mainland population of the Javan rhinoceros in Vietnam: the very distinctive Bili apes, the largest and strangest of the chimpanzees: and huge populations of two African giants, lowland gorillas and elephants.
Seriously, we missed a hundred thousand gorillas. Searchers for the dinosaur-or-whatever Mokele-Mbembe might be have not found the animal, but they have demonstrated how damned hard it still is to search the least-known regions of the world. So reports of big animals in Africa and South America, like the true pygmy elephant, African mystery apes (those in particular, given the recent primate finds there) and Van Roosmalen's black-and-white jaguar, can at least be seriously considered, although the standard of a widely accepted holotype (see here about the elephant) has yet to be met. Certainly there are some areas on the Asian mainland, in Siberia and the Pamirs to cite two examples, where's it's not impossible further large species are hiding.
(I am, BTW, setting aside here the new species described from reinvestigations/reclassifications of existing specimens. New wild pigs pop up a lot this way.)
Than we get to the specific case of North America. After throwing out the most recent of the 86 species of brown/grizzly bear the splitters of past centuries erected, we have exactly zero species new large animals from the 20th or 21st centuries. The best we can do for recent rediscoveries is the population of wood bison found in 1957 in Canada: significant, certainly, but having occurred 65 years ago, not nearly as significant as it used to be. Gerald Wood, in the popular (and still most enjoyable) book Animal Facts and Feats, told of an unusually large strain of grizzly bears found in Alberta in 1960, but I can't find a more scientific source on that. You could sort of argue that finding brown/polar crosses in the wild, first done in 2006, is sort of like finding a new animal, but we don't know when those crosses began to occur, so I'm setting that one aside, too. A little better case could be made that the onza counts: while this strange-looking, long-legged puma has in fact been DNA-typed as a strange-looking, long-legged puma, it is an animal with a distinctive look and was reported many times from Mexico and dismissed until there was a specimen in hand in 1986.
And this brings us to sasquatch. There are other large cryptid species reported or suspected from various regions of North America, from the giant beaver to the dire wolf, but in none of these cases is the evidence remotely comparable to the hundreds of sightings of sasquatch. I realize I'm going in to opinion here after sticking to hard facts, but the chances of big hidden mammals existing on this continent is inevitably a judgment call, and I don't think it looks very likely. I think that if we are going to find any new species of large mammal on this continent, it will be sasquatch - the others, aside from the occasional curious report, are not well supported and are going to fade out. (Where are the giant beaver lodges and dams? Why would the dire wolf have survived the rise of such successful modern predators as the wolf and the puma?) If sasquatch is not hiding in N. America, no big animal is.
We have large forested patches, mainly in the Pacific Northwest, where the trees stretch many miles over rough terrain and few humans have yet trodden. I'll accept Pyle's book Where Bigfoot Walks as answering one big question - is the habitat suitable for a reported type of animal? (The answer: it's not perfect, but Pyle argues an omnivore might survive in pockets against its major competitors, humans and bears.) But hiding gets hard. It gets harder over time. Despite our wilderness areas, this is not Africa or the Amazon basin (which are, themselves, increasingly intruded on). The U.S. not only has increasing numbers of loggers, foresters, hunters, birders, and developers going into the woods, but there are no towns or hamlets and few houses in this country exempt from instant electronic communications with larger populations: phones and internet are nearly ubiquitious, and roads suitable for autos connect even the most rural habitations. Of course, witnesses may see sasquatch, think about possible ridicule, and not report it, but the stigma is fading as TV and internet bring more programming on cryptozoology in general and squatch in particular. My feeling is theat the likelihood of a good sighting without a followup, though this is unprovable without a massive surveying effort, is going down.
This doesn't mean sasquatch can't still be hiding. There are unsolved sightings. There are some intriguing footprint trails. But I think on balance there is either one big hidden mammal in North America, or there are none. I am hoping for one.