It's entirely possible, depending on your conception of newspaper. There will always be a place for the local paper, with stories about weddings and community events, but to put out a paper like the New York Times or the Washington Post is a tremendously expensive proposition. This is because of talent and the need for original, non-local reporting (i.e., bureaus). Simply put, talent (at least, well-known talent - there's plenty of talented unknowns that can be had for the cheap) costs big bucks (I think of the excellent Atlantic Monthly and reports that it is losing millions annually), and so does the maintenance of bureaus.
I bring this up because there's been a bit of a blogstorm lately regarding new figures that show a steep decline in newspaper readership (1.9% in the last six months). Power Line and The Bernoulli Effect, among others, have been considering the reasons, as has the Wall Street Journal. (Jeff at T.B.E. has a good mini-discussion in his post about why you can almost be certain that most of the left's conspiracy theories are false, and it's a view I've always subscribed to myself - in short, if they were true, the MSM would be over them like flies on - well, on that stuff flies like to get on).
The Power Liners attribute part of the drop to more conscientious recordkeeping to avoid scandal, and that certainly seems sensible when you consider the wide disparity between the drops at different papers. I must say, though, that I think there's a lot to the notion of the WSJ and Rupert Murdoch that the Internet may do to the newspaper what cars did to the horse-and-buggy industry.
As I alluded to earlier, I don't see papers completely going away, just becoming more local, or, for the ones that need a national presence, more reliant on wire services, piecework, and perhaps less frequent publication. As strange as it may seem, a viable business model for, say, a Wall Street Journal might be a one section daily (headlines, stock quotes, editorial, but no in-depth features - and no real 'marquee' journalists), with a large amount of supplemental subscription-only web material (which they're already moving towards), and a weekend only section that contains all the splashy, 'name' reporting.
While you can see part of this transition already taking place, it's painfully obvious to me that the big-time papers can't conceive of getting rid on the 'daily' - yet, in my view, it's the daily print paper that they can't afford to keep, at least not in its present state. If I were an investor in print publications, I'd be looking to diversify - and quickly.