New Orleans is eliminated from first place.

To show that New Orleans is eliminated from first place, we start with the current conference standings:
            Team	W	L	GL	PCT	GB
   Oklahoma City	68	14	0	0.829	0.0
         Houston	52	30	0	0.634	16.0
          Denver	50	32	0	0.610	18.0
     LA Clippers	50	32	0	0.610	18.0
       LA Lakers	50	32	0	0.610	18.0
       Minnesota	49	33	0	0.598	19.0
    Golden State	48	34	0	0.585	20.0
         Memphis	48	34	0	0.585	20.0
      Sacramento	40	42	0	0.488	28.0
          Dallas	39	43	0	0.476	29.0
         Phoenix	36	46	0	0.439	32.0
        Portland	36	46	0	0.439	32.0
     San Antonio	34	48	0	0.415	34.0
     New Orleans	21	61	0	0.256	47.0
            Utah	17	65	0	0.207	51.0
           Total	638	592	0

New Orleans can finish the season with at most 21 + 0 = 21 wins and will finish the season behind the following teams:
Oklahoma City has already won 68 games.
Houston has already won 52 games.
Denver has already won 50 games.
LA Clippers has already won 50 games.
LA Lakers has already won 50 games.
Minnesota has already won 49 games.
Golden State has already won 48 games.
Memphis has already won 48 games.
Sacramento has already won 40 games.
Dallas has already won 39 games.
Phoenix has already won 36 games.
Portland has already won 36 games.
San Antonio has already won 34 games.