This article describes the expectations that most Americans have about the presidency. It argues that Trump has not met the key expectations. Therefore, we have not had a real president in the White House. Trump does not need to resign because he has never assumed the role of the president. The presidency is vacant.
Of course, we do have a person who regards himself as the president of his base which includes white supremacists and neo- Nazi's among others who hope that he will "drain the swamp". Many Americans who believe that Trump has filled the swamp with inexperienced and poorly motivated officials, hope that he will be impeached. Frankly, I would not be totally surprised if he decided to resign. The Special Counsel, who is investigating any connections between Trump's campaign and Russian interference in the election, is likely to uncover unsavory financial connections and deals that could have a profound affect on Trump's brand and his business empire. He may decide to resign in order to protect his business interests in return for ending the investigations if he is given that opportunity. Even if that does not happen, his performance in office has already badly damaged his brand. Many of Trump's real estate holdings are not performing as well as they did before he assumed office. Most of them are heavily leveraged with loans. It will be more difficult for Trump to service his debt obligations under conditions of declining revenue.