So from reading the mod author's last notes, it seems that Fallout New Vegas Archive Invalidation Invalidated a) is no longer supported by the creator and no longer works with the latest official patch.
http://newvegas.nexusmods.com/downloads/file.php?id=35935#content

Furthermore, comments in the forum at the nexus site seem to indicate that the built-in invalidation feature in Nexus Mod Manager also doesn't work.

Step 3 in NMC's texture pack states that this step is required:
"3) IMPORTANT: Activate "archive invalidation invalidated" so the new files show up in game. (Also, if you are overwriting a previously installed, different sized pack, THEN TOGGLE ARCHIVE INVALIDATION INVALIDATED OFF, THEN BACK ON AGAIN or the new textures may not show up)
You can activate this in the Fallout Mod Manager Mod (FOMM)
or by using the Archive Invalidation Invalidated mod:"

I am unable to get FOMM to run at all (crashes immediately upon startup), so it looks like I need the Archive Invalidation Invalidated mod.

Can someone explain how to accomplish this step? Thanks.

I have the latest version of Nexus Mod Manager (.15.8) installed.

I use the FO3 version, but someone did one for New Vegas later on. I don't know if it works the same as I haven't used it. But, just download the file and follow his instructions on the page - http://newvegas.nexusmods.com/downloads/file.php?id=37004.
Any time you add a new texture to the game you don't need to "toggle" anything. It does it automatically. Somehow I also don't use FOMM's archive invalidation and don't need to because of this way.