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	42	13	27	0.764	0.0
     San Antonio	39	16	27	0.709	3.0
         Houston	34	20	28	0.630	7.5
          Denver	35	21	26	0.625	7.5
       Minnesota	34	22	26	0.607	8.5
       LA Lakers	32	21	29	0.604	9.0
         Phoenix	32	24	26	0.571	10.5
    Golden State	29	27	26	0.518	13.5
     LA Clippers	27	28	27	0.491	15.0
        Portland	26	29	27	0.473	16.0
         Memphis	20	33	29	0.377	21.0
          Dallas	19	34	29	0.358	22.0
            Utah	18	37	27	0.327	24.0
     New Orleans	15	41	26	0.268	27.5
      Sacramento	12	45	25	0.211	31.0
           Total	414	411	405

New Orleans can finish the season with at most 15 + 26 = 41 wins and will finish the season behind the following teams:
Oklahoma City has already won 42 games.