Yes, the media has influence but the power of the press is small compared to the power of an experienced con artist. The press can only "tilt" the truth a bit as they are legally viable when a lie is given (like FOX having to pay $770 million for the lie they spread). Con artists, especially like Trump being president, do not have to stick to any kind of truth as the only thing they face legally is impeachment and with them holding the Senate, impeachment will never happen.
Oh and by the way and talking of the press, isn't biased-for-the-right FOX the biggest media in the U.S.?