No. The landlord cannot charge you any fees or interest if you choose to enter into a payment plan.
The landlord can turn you down if the total amount of deposits and nonrefundable fees are not more than 25% of the first month’s rent, and the landlord is not requiring you to pay the last month’s rent when you move in.
The landlord can start an eviction lawsuit (called an unlawful detainer action) against you by serving you with a 14-day Pay or Vacate Notice. It’s treated as if you didn’t pay your rent. Read Eviction and Your Defense.
If your landlord turned down your request to pay in installments, you miss a payment, or your landlord starts an eviction action against you, try to get legal help right away.