UNLV, Boise State and Nevada should be in consideration for a NIT bid. All of these teams are probably not getting in, but one or even two have a shot.
The NIT is a bit different in that it awards and auto bid to the regular season champion if they do not qualify for the NCAATournament, and so far there are 11 autobids out of the 32 spots.
However, when looking at Bracket Matrix's projections there are zero Mountain West teams in the mix, and only Boise State is being considered. This comes as a shock since both Boise State and UNLV have passed the 20-win mark.
The next rung of tournaments are the CBI and the even lower CIT. In those tournaments teams pay their way in and also if they choose to host any games.