Interestingly, he tweeted that out shortly after CNN has discussed that very portion of the story about the President watching CNN, MSNBC, and hate watching Don Lemon. But that's besides the point. He denies it.
What is interesting to me is that multiple people inside the White House tell me they worry about the President's friends and staff talking to Maggie Haberman, the reporter who wrote the piece. On at least two separate occasions, including once with people working for the President's response to the Mueller investigation, people in the White House have told me they get very frustrated by White House staff and Presidential friends talking to Haberman and, despite multiple demands that it stop, it has continued. That makes this story more credible in my mind.
What is most striking about the story to me is that Mrs. Trump is nowhere to be found in it. The President starts watching television before dawn, from his bed, which suggests she is not present. There is also no mention of his youngest son. Here's why that is striking to me -- family tend to be the closest support group for anyone, particularly the leader of the free world. But it seems the President is not often surrounded by his family as a source for comfort. He reaches out to others by phone and chats with them, some who clearly hope to rile him up on various news.
If the President is not relying on his wife and spending time as part of a regular routine with his family, that's not a good or mentally healthy thing and I hope his family will work to have more family time with him.