Likewise, if you are concerned about how much you don't know, you may be fearing the system and assuming the worst. I'm not calling you out or anything, this is basic human nature and something that we all do at some point.
Carbs ARE fairly simple devices. They are more or less just calibrated air leaks and calibrated fuel leaks. They generally don't just fall out of calibration for the hell of it. This is why the standing joke/rule of thumb is "it's always the ignition", the ignition system is the bit with parts that wear out and break down, not the carburetor.
Back to original point, if you have fear of a system due to percieved lack of knowledge, you may avoid it altogether because it all seems like a Black Box. But let's review: The idle is too low, and it stalls.
It's stalling most likely because the idle is too low. The idle speeds are set just high enough that the engines don't stall, therefore if the idle speed is too low, it may stall.
Idle speed is controlled by ignition timing and how far open the throttle plate is, just like if it were EFI. Curtis raised a good point, "it's always the ignition", did the distributor get moved? A timing light will tell you for sure. It probably should be checked anyway, just to rule anything out BEFORE you mess with anything else. What's the first rule? It's always the ignition 
Another point, which is highly unlikely since you didn't mention that the engine seems to really lack power, is if the timing chain skips a tooth, you will notice this by the ignition timing being REALLY far off, like 15-20 degrees off, and no evidence that the distributor had been moved. But, again, you'd also have mentioned that it now doesn't have enough power to peel the skin off of warm pudding, so highly unlikely. Still want to check the timing to verify timing.
If that checks good, or adjusting it makes it worse, then it is time to see why the throttle is too closed. Could be because something that used to stick and hold it open is no longer sticking. Could be a buildup of gunk in the throttle bore is blocking airflow, although this generally takes a long time and is highly uncommon on a carb what with the fuel flowing past it. As also mentioned upthread, hitting everything with carb cleaner, inside and out, is a good place to start if only because it lets you see what you can see instead of seeing a mass of Stuff covered by a layer of goo and grime.
Carburetor problems usually result in weird drivability problems, not idling too low. One thing that can happen is the idle speed screw can back off... which is simple, obvious, and you'll never see it if you don't look at it
