There have been a number of turret-based builds here on the forums, but they all seem to question the viability of this approach. I can say conclusively that this works to a point; you won’t be raiding with these, but they are capable of handling some of the heavy hitters in your local mobs by themselves. At OP3, the turrets kill enemies at a rate that I find unusually fast for that far into the game. Bullyrotts, WAR, Angel, and SGT Loaders, Bone Crushers and Scavengers… just tested this out to confirm that they all die relatively easily. Here’s how:
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First, here’s the build I used. Nuke hits surprisingly hard: a little less than 2 million for armored targets, a little less than seven million for flesh targets (both pre-slagged), so I definitely wanted that. The choice then came down to Double Up or Gemini, and I figured that they were kind of a wash: one adds two guns to one turret, where the other is one gun on two turrets (if there’s more math to this, let me know), but Gemini allows me to get Resourceful, place them in potentially strategic positions, and it lets me apply Nuke twice. Since the turrets will be doing the killing, I will be doing the slagging, so my character just loads slag weapons.
If you can’t tell from the highlighted skills, I’m using an Auto Gunner COM. This is, I believe, the only COM that can increase the turrets’ damage output (by increasing their fire rate) as opposed to just extending their duration. They can easily outpace enemy health regeneration, and in practice, it occurs to me that I might be able to get away with an Engineer COM: the increase in fire rate gives you more damage output than longer sentry time with standard fire rate, but the Engineer COM comes with way more side benefits.
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Second, here’s the technique. Pre-slag the targets. I used a slag Singularity to get enemies grouped together to facilitate hitting as many as possible with both Nuke shots. Then just run around the fight and focus on keeping enemies slagged; without slag, their health regeneration may outpace the turrets. If you’ve grouped or isolated the enemies properly, they won’t focus on you, and you can just focus on keeping them slagged while the turrets get the kill. If you’re so inclined, you can switch to an actual weapon and help drop the enemies, but the idea here is to let the turrets do all the work.
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Third, here are some other considerations. I used a Cooldown relic. It doesn’t appear that an explosive relic helps Nuke, and I can’t think of any others that help with them? I’m not sure if holding the Little Evie while your turrets get a kill count towards the cooldown (and I want to be slagging mostly anyway). A slag Transfusion will help keep the turrets health up, but in practice, it’s just enough to shave off some of the incoming enemy damage. Still, it’s a reliable area slagger, and the health is just bonus points. BAR does not seem to make much difference in the turrets behavior? Those skills seem to apply to the Commando, not his turrets.
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Fourth, here are some things to watch out for:
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Enemies behind cover that you could easily shoot are tough for the turrets to hit.
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ION Loaders’ shields keep the turret fire out and prevent you from slagging the group within. Usually, I’ve tossed the turret very close for Nuke to hit, which puts the turret within the shield, where the ION loader zaps it. Watch for that.
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In retrospect, I may consider grabbing Onslaught, since turret kills activate this, and the movement speed is handy for dodging enemies that have it out for you instead of the turrets.
edit - some keyboard shortcut inadvertently posted this before I was ready, but this is basically it. I’m still testing some things, and may add a video later.
2nd edit - trying a very sketchy build with +5 in Laser Sight. What?! Yeah… I might be noticing a difference at mid range. Also, how does Geminuke sound for this build? Awful? Even better. 
3rd edit - turns out the Slayer of Terramorphous doesn’t enhance the Nuke-derived burn DoT. Oh well…
4th edit - field notes:
- Rabid Stalkers and Skags - no problem; they stay point blank on your turret, so eat all the damage.
- Pimon and Tumbaa? Pimon isn’t a problem once you get his shield down (so the turret can see him), but you do have to corner and separate them individually.
- The turrets couldn’t kill an Ultimate Badass Loader with their guns (although they dropped him to just a sliver of life). A Nuke follow up polished them off.
- PWR and BUL Loaders will reflect the bullets if their shields are up, but if you Nuke them into melee range in a corner, they’ll drop their shields and will fall.
- Threshers are a real problem, mostly because they keep washing off the slag by burrowing, which burns off sentry time.
- Laser Sight… I’m not sold yet, but it may not have been working right (I couldn’t see the full beam, just the first foot or so of green haze.
- Varkids are okay up to Super Badass versions, because, again, they tend to burrow to wash off slag which burns off sentry time. Still, I did drop one with a few applications of Nuke.
- I think I’m also sold on the Engineer COM because Nuke is producing more damage per re-application with the huge cooldown (fire Nuke then immediately recall) than the weapons are with an Auto Gunner COM running for a full standard-length time.
- Nuke was reliably one-shotting slagged Surveyors and Rakk that came within range. I didn’t come across any Super Badass versions though.
- Nuke + turrets took out a slagged shock Ultimate Badass Skag in one go (and I was sure they wouldn’t). They did have him pinned, and he didn’t use his shock beam on them though. Nuke is awesome.