Earlier this week, I watched the Marx Brothers'
Room Service (1938). "Monkees in Manhattan" shares the same basic plot and a number of specific elements.
In Room Service, Groucho Marx plays Gordon Miller, who's been staying in a hotel while trying to put on a play. The management continually threatens to throw him out because he owes $1,200, and he has to stall until he can get financial backing for his play, which he'll use to settle his debts to the hotel. One of the strategies he uses is to fake an illness; he reasons that the hotel can't throw out a sick man. Harpo, as Miller's assistant Faker, blows iodine through a colander onto the face of Leo Davis, the play's author (played by Frank Albertson), to give the appearance of measles. In an-other scene, Miller promises to consider one of the hotel waiters for a rôle in the play in exchange for the waiter's delivering some food to the room.
In "Monkees in Manhattan," the Monkees go to New York to star in McKinley Baker's Broadway show based on them. Almost as soon as they arrive at his hotel, the hotel manager appears and tells Baker that he's tired of waiting for the rent and that Baker needs to leave in an hour. Baker explains to the Monkees that in three hours, his backer will give him a check, which he can use to pay his debts, and he sneaks out to retrieve it while the Monkees hold the room. As in Room Service, they feign an illness: Micky claims that Peter, with dots drawn on his face, is suffering from the plague. Later, when the hotel manager tries to starve the Monkees out of the room by refusing them any more room service, Mike convinces a waiter that he would be perfect for the rôle of a prince in a Broadway musical and that his first step in show business should be to deliver food to the Monkees' room.
There's a note in the credits of Room Service that it's based on a play (by John Murray and Allan Boretz), so it's possible that "Monkees in Manhattan" is drawing upon that rather than the movie, but the similarities are clear.