Is there a console command to make NPCs completely idle, stopping their daily routines?

I don't know if there is a console command but it can be easily done in the GECK.

You could try removescriptpackage - whatever current AI package they're doing will be stopped. Though if you want to remove them all I don't know if there's a way (outside the GECK) to see how many AI packages they have.
After "removescriptpackage" "evp" will make them reevaluate their packages and pick the next one in the list. If they don't move, or don't do anything it should be safe to say they have no more.

After re-reading, or if you want to freeze someone in place, TAI (Toggle AI). To freeze everyone, including yourself (that's not avoidable afaik), go into third person and type TFC 1. Handy for action screenshots

There's one, 'setunconscious', that puts individuals to sleep, I believe. I tried it on my courier and she closed her eyes (she remained standing) and I couldn't make her move via the movement keys anymore.

Also, there's three pages on the wiki of all the console commands available. Perhaps that might help you.

http://fallout.wikia.com/wiki/Fallout:_New_Vegas_console_commands

http://fallout.wikia.com/wiki/Fallout_3_console_commands (most/all seem to still work in NV)

http://fallout.wikia.com/wiki/Gamebryo_console_commands_%28all%29 Not all of these will work.

you can hit the console click on the person you want to freeze and use TAI on them only too mysty.

For the record RemoveScriptPackage only removes packages added by AddScriptPackage. Packages added to the NPC in the editor can not be removed by using the console, or even by a script. NPCs can also only have one package added by AddScriptPackage, calling AddScriptPackage again will remove any ScriptPackage the NPC is currently following, and replace it with the new one.

Thanks for the replies, everyone. 'TAI' is the only one I can get to work, though. TAI makes them completely frozen in place, but it will have to do until I become more savvy with the GECK.