Axios reports believable if depressing results from an on-line poll of nearly 5000 people by Survey Monkey conducted June 30 - July 3. In brief, Republicans by 89 to 9 percent trust President Trump more than the news network CNN, while adult Americans in general trust CNN more than Trump by 50 to 43. Independents prefer CNN by 55 to 40 and Democrats by 91 to 5. (The remaining few percent didn't have an opinion.)
CNN has its problems, from obsessive coverage of single Big Stories to some sloppiness in its reports in specialized fields, but we're talking about relative trust here, and it's hard to see how anyone can rate Trump more reliable than CNN. It's a major problem for American democracy when people don't just have differing opinions but differing conceptions of reality. I don't mean to suggest that Democrats are necessarily well-informed about everything either, but ...
(Incidentally, while on-line polls in general can be questionable and subject to manipulation, Survey Monkey takes steps to avoid those problems and has a respectable track record, for example producing the most accurate polling on the Brexit vote in the UK, according to fiverthirtyeight.com. For more on Survey Monkey see this article from the Los Angeles Times.)
Meanwhile, Politico reports that condemnation of the news media by Trump and others has led international organizations such as the Committee to Protect Journalists, Reporters Without Borders, and the Reporters Committee for Freedom of the Press -- which normally address threats to reporting by governments and criminals in other countries -- to express concerns about dangers to reporters here in the United States from people who believe the media are deliberately lying to them.by