I believe Charles Keller at the New York Times proposed just such an idea. The government would grant newspapers exemption from anti-trust regulation (not sure what concessions would be extracted in return), basically to allow newspapers to survive as quasi-nonprofit entities.
In the long run, monetizing their popularity has to involve making people pay for the value the newspaper adds. There are two present problems with this.
One is that so many news outlets across so many types of media are chasing the same story (national politics, sports, celebrity news, etc.) that the news is overly available, so there's actually very little value being added by any given newspaper. That's a simple problem of too many competitors for the market and normal market consolidation should sort that out.
On the other hand, there are plenty of other important things to report on in a serious newslike way, and these are really going to suffer for the death of the mainstream newspaper. For example, for Dana Priest to break the story on CIA detention centers took months of work on top of a career's worth of sources and contacts. The problem is that there are precious few examples of people doing this depth of work as an independent journalist. That said, Murray Waas is a pretty interesting case in this area - he does basically seem to work for himself, and he often finds out stuff that others don't know yet. But he's a bit prone to going off on people or otherwise ranting, and a number of his assertions have not panned out.
Blogging on hearsay or newspaper articles one has read (i.e. the business model of Slashdot and nearly every politics blog on the planet) does not constitute journalism. Doing background research cultivating multiple sources on a subject, fact-checking, and editing to ensure (or at least attempt) an objective approach are journalism, and they are time-consuming, often boring efforts. As in every other kind of business, getting people to have the discipline to do the unfun stuff day after day requires paying people. Otherwise, people just do the fun stuff. So until someone can show me how independent citizen journalism deals with this problem, my own view remains that it's unproven as a business model.