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	56	15	11	0.789	0.0
     San Antonio	53	18	11	0.746	3.0
       LA Lakers	46	25	11	0.648	10.0
         Houston	43	27	12	0.614	12.5
          Denver	43	28	11	0.606	13.0
       Minnesota	43	28	11	0.606	13.0
         Phoenix	39	32	11	0.549	17.0
     LA Clippers	35	36	11	0.493	21.0
        Portland	35	36	11	0.493	21.0
    Golden State	33	38	11	0.465	23.0
     New Orleans	25	47	10	0.347	31.5
         Memphis	24	46	12	0.343	31.5
          Dallas	23	48	11	0.324	33.0
            Utah	21	50	11	0.296	35.0
      Sacramento	18	53	11	0.254	38.0
           Total	537	527	166

New Orleans can finish the season with at most 25 + 10 = 35 wins and will finish the season behind the following teams:
Oklahoma City has already won 56 games.
San Antonio has already won 53 games.
LA Lakers has already won 46 games.
Houston has already won 43 games.
Denver has already won 43 games.
Minnesota has already won 43 games.
Phoenix has already won 39 games.