Assuming liberal bias in the media is true, should we demand a government sponsored newspaper and network?

Answer 1

That is a ridiculous question. Freedom of the press is established by the Constitution. It is up to the individual and each media organization to uphold the reliability of its reporting. And if we had government run media, would it not slant in favor of the party that was in power? Your best bet is always to get information from multiple sources and do research on things that may have differing conclusions (global warming).

Answer 2

A free press is considered important to keep transparency in the government and keep the Government responsive to the public.
A modern usage of the press as the "Fourth Estate" is used to identify it as equal in importance to the Executive, Congress and Courts...so no, it has a role outside the government.

That the press offends conservatives and other proponents of obedience and reverence to the state, just indicates that the press is doing it's job.