I'm not sure where to put this topic, but this seems to be the most suitable.

Every merchant I've encountered since I first started the game (188 Trading Post, Good Springs General Store, Gun Runners, Crimson Caravan) has not updated their items, and I'm level 15.

They all have 0 caps because I've sold my loot to them, and they all still have weak weapons and ammo.

Have I just not leveled up enough, or is this a game breaking bug that will force me to start a new game?

On the pc version sometimes, cause the game always starts on Sunday, they don't seem to refresh every 3 days like they should. You can try:

stand in the actual same room/area near the merchant, save the game, exit the game (to desktop), restart the game, load game. Sometimes that resets it for some people.

Try completing a main quest (or a portion of it). I noticed in my game the merchants often update their items after that happens.

I had the same problem with Goodsprings merchants. But when I met Cliff Briscoe at Novac, that seemed to "fix" the bug.
My suggestion is: try to look for a new merchant. Sell him/her something. Wait 24hrs and check his/her inventory and caps. If the merchant still hasn't refreshed his/her inventory, wait 24hrs more. Repeat these steps until you waited 6/7 days (usually the merchant refreshes his/her inventory afrer 24/48hrs). If after 6/7 days the merchant has still the old inventory and caps amount, you had the bug: reload the save and try again.
Otherwise, if the merchant refreshes his/her inventory, save the game (but not overwrite the older save!) and go check the other merchants, everything now should be right and you won't meet the bug again for the rest of the game.
This is what happened to me.

Do you have the most recent patch? I noticed I had this problem with a couple vendors (the Van Graffs namely), the patch fixed it.

Ok, everything is working now. I just slept for 3 days straight without talking to anyone or doing anything.

Thanks for the suggestions.