This is not a suggestion for "single payer" journalism. Private media companies would continue to operate. We'd just be setting up a complementary and competing "public option", similar to the public option for health care.
The hybrid option
Another option is to fund not a monolithic national news source, like the BBC, but rather multiple competing news sources. Two analogues are public financing for campaigns, in which any candidate with sufficient support obtains government funding, and Medicare: public funding with private delivery. Similarly, under the hybrid approach, a producer of investigative journalism could obtain government funding, via grants or tax benefits, provided it demonstrates sufficient professionalism and endorsement by consumers.
President Obama recently expressed openness to a bailout of struggling news organizations. He said he might support tax breaks to news organizations willing to restructure as nonprofits.
Compared to the public option, the hybrid option has the advantage of promoting a greater diversity of viewpoints. It also builds on the expertise and infrastructure of existing media outlets.
Libertarian qualms, progressive responses
A libertarian would argue as follows: Government is inefficient, and it's usually corrupted by special interests. Furthermore, if there is demand for news and investigative journalism, people will be willing to pay for it. Indeed, Americans donated over a billion dollars for the 2008 elections. So why don't people just pay, or donate, to the news sources which best match their political persuasions and self-interests?
First of all, it's worth repeating: a strong independent press is a public good, like the police, and unless people are forced to pay, via taxes, they will freeload on others.