The question is not if it will break the government. The question is if the government should be in the business of funding television in the first place and particularly if the government should be funding news.
The clear answer here is a resounding no IMHO. There is no reason for the government to be funding news or entertainment.
Or education? Do you believe we are a democratic republic? A nation whose population votes to elect their representatives fits that definition, notwithstanding the myth and meme that the United States is not a democracy.
That said, a democracy needs an informed and educated population to be and remain a nation of The People, by the People and for the people. Both NPR and PBS provide more than news and entertainment - they provide many things and most are informative, educational, substantive and relevant to the lives of voters and soon to be voters (i.e. minors).