If my husband threatens that he will leave me or kill himself because i haven't done something right is that abusive?

You should tell someone straight away, and persuade him not to kill himself, if he is doing this, you do not want to be with him for your life, you need to get rid of him straight away.

Yes it is abuse, that is called emotional blackmail. He needs to get some form of counselling, before he either hurts you or himself. Eventually you'll start to have low self esteem, once that happens, you'll find it very difficult to do normal everyday things. Often in these situations, the relationship will turn violent. There is no easy way of saying this, if your strong enough to do it now, get out of the situation totally.