It is said that a broken promise is an act of aggression. To elaborate: when someone promises to do something and doesn't follow through, that person is saying 'screw you.'
The natural reaction is to feel angry when you find yourself on the receiving end of a broken promise. When you take the bait and become furious, the person who has broken his/her promise is actually glad. Your angry reaction proves that he/she got you.
What is fascinating is the fact that the anger that you feel is actually induced anger, meaning that it is the other person who is angry and not owning it. By behaving in hostile ways (broken promises classifies as hostile behavior) the other person forces you to carry his/her unwanted aggression. You become an emotional toilet bowl, and each time you blow a gasket the other person feels relieved--your release of anger gives him/her a vicarious sense of release; he/she doesn't need to own his own anger, since you are expressing it for him.
The only way to get around this fix is to stop carrying your husband 's anger. This is easier said than done, since his behavior is so infuriating. The only way around this bind is for you to refuse the promise as soon as it's offered. This will rip the rug out from under him. He can't anger you by yet another broken promise, if you refuse to accept the promise. This tactic should enrage him, which is just fine. Let him own his own anger and stop using you to carry his unwanted feelings for him.
I know that you will be thinking at this point: great, so now I am going to let him off the hook all together by not expecting him to do any chores. The fact is that he isn't doing the chores anyway, so you have nothing to lose by changing tactics. In fact, he may be not doing chores because you are locked in a vicious cycle that is enraging him even more.
What do I mean? Stay with me and I will spell it out: You are furious at him for his broken promises. You let him have it, he resents you and what does he do; he gets even by delivering yet another broken promise. After a while you don't know which came first, the chicken or the egg: At this point we have to wonder if he is breaking promises to pay you back for your giving him hell over his last broken promise.
The only way to break the vicious cycle and stop fueling his paybacks (the broken promises) is for you to step back and stop playing the game. Don't accept any promise. In fact, tell him that you have come to realize that he isn't capable of keeping his word, so you don't expect that he will do the garbage (or whatever else he promises to do).
If he is the type of person I think he is (spiteful, contrary), he will do the garbage just to show you how wrong you are. This technique will accomplish what you want: to get him doing chores and keeping his word. Let me know how you make out.