I just went through the same problem on my 67 SS350. It started out as a random misfiring at idle and a backfiring problem under WOT. Eventually, deteriorated to not being able to start it at all. Given the backfiring problem under load, I was thinking ignition. I checked a few plugs, was getting spark, so I decided to go through the carb too. No change. I was thinkiing that the points/condensor - although old (12 years +, 1000 miles) should be ok, right? Never heard of a condensor going bad.
After letting the car sit for most of this summer (just didn't feel like working on it - too busy), I finally bought a set of points/condensor/rotor, took 5 minutes to install them, and the engine fired right up. Runs great now, all issues resolved. Oh well, carb freshening didn't hurt as the car does not get much use. I feel a bit silly for letting the car sit idle all summer for such a simple problem. Now - trying to get as many drives in as possible before the Michigan winter arrives!