Can I secretly kill every guard in a town?

Is it possible to kill all of the guards in a town? Ideally, I'd like to do this secretly so the entire town doesn't see my deeds and put a bounty on my head.

Edit: I was questing in Markarth and was told by a guard to back off and stop being nosy. I didn't and when I went to the Shrine of Talos I was set upon by a bunch of guards. Now I have a huge bounty and I had to sneak/kill my way out of the city. Every time I killed a group of guards the bounty was reduced by $1000, but I still have a $30,000 bounty.

I haven't even been through 1/3 of the city yet and know there has to be a lot of quests, so what do I do? The only solution seems to kill every single guard (and inhabitant).

So, this is a classic case of asking the wrong question. Guards will respawn, and unless you want to give up on the Reach for good, you'll need to resolve this. You can't slaughter your way out of this one. Well, at least not without letting them haul you in first.

After finishing The Forsworn Conspiracy quest, being arrested is the only real resolution. This triggers the quest No One Escapes From Cidnha Mine, which is short, offers some great rewards, and will clear your bounty in Markarth.

If guards in Markarth will no longer accept a yield, your best bet will be to reload a save prior to the wholesale slaughter of innocent militiamen.

Yes, you can. Just sneak attack kill them in one hit with no one around to see or hear -- or reverse pickpocket poisons onto them with the "Poisoned" Pickpocketing perk.

However, the guards will respawn, so the "unguarded" condition of the town is only temporary.