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	61	16	5	0.792	0.0
     San Antonio	59	19	4	0.756	2.5
       LA Lakers	50	27	5	0.649	11.0
          Denver	50	28	4	0.641	11.5
         Houston	48	29	5	0.623	13.0
       Minnesota	46	31	5	0.597	15.0
         Phoenix	42	35	5	0.545	19.0
        Portland	40	38	4	0.513	21.5
     LA Clippers	39	38	5	0.506	22.0
    Golden State	36	41	5	0.468	25.0
         Memphis	25	52	5	0.325	36.0
     New Orleans	25	53	4	0.321	36.5
          Dallas	24	53	5	0.312	37.0
      Sacramento	21	57	4	0.269	40.5
            Utah	21	57	4	0.269	40.5
           Total	587	574	69

New Orleans can finish the season with at most 25 + 4 = 29 wins and will finish the season behind the following teams:
Oklahoma City has already won 61 games.
San Antonio has already won 59 games.
LA Lakers has already won 50 games.
Denver has already won 50 games.
Houston has already won 48 games.
Minnesota has already won 46 games.
Phoenix has already won 42 games.
Portland has already won 40 games.
LA Clippers has already won 39 games.
Golden State has already won 36 games.