Does Landing At Bottom of Small Staircase Need to be 36" Long
Assuming you're doing residential work, the 2012 IRC specifies (source):


  R311.7.6 Landings for stairways. There shall be a floor or landing at the top and bottom of each stairway. The minimum width
  perpendicular to the direction of travel shall be no less than the width of the flight served. Landings of shapes other than square or
  rectangular shall be permitted provided the depth at the walk line and the total area is not less than that of a quarter circle with a
  radius equal to the required landing width. Where the stairway has a straight run, the minimum depth in the direction of travel
  shall be not less than 36 inches (914 mm).
  
  Exception: A floor or landing is not required at the top of an interior flight of stairs, including stairs in an
  enclosed garage, provided a door does not swing over the stairs.


So yes, your landing depth would need to be at least 36" or the width of your staircase, whichever is greater. The listed exception isn't relevant as it only applies to the top of the stairs, not the bottom. I don't know if this has changed in more recent versions of the IRC; also, your house might not be subject to the same rules, so check with your local inspector.