Sometimes people try to broaden it by talking about giving of "time, talents or treasures," but besides being obnoxiously alliterative, there are times in life when one not only doesn't have cold hard cash, one doesn't have time, either, and one's talents have shriveled up from sheer exhaustion. Discussions about giving can just be another paper-cuts-and-lemon-juice reminder of how little you have to give and therefore how unspiritual and disobedient you will have to continue to be (and, perhaps, how badly you must have sinned to be in that position, whether you can figure out an offense or not).
First of all, the emphasis on the New Testament is on giving out of abundance, which I submit right off the top should mean that no one should feel that they ought to be giving if they genuinely don't think they can afford it. People are supposed to give as God has prospered them (I Cor. 16:2), not 'till it hurts.
But I think we may be missing an even more critical point about giving, which is "Why?" God doesn't need our money. He's got the cattle on a thousand hills and the whole world in his hands and all that. Nope. Not for God.
Some people talk about it being for us, so we can remember that everything belongs to God, and that may be part of it. Some people think it's so that God can give us more stuff, and they're just wrong.
But in the New Testament, when it talks about giving, it talks about a different reason: for unity and fairness within the body:
For I do not mean that others should be eased and you burdened, but that as a matter of fairness your abundance at the present time should supply their need, so that their abundance may supply your need, that there may be fairness. 2 Cor. 8:13-14.
And yet, sometimes that is what God has blessed us with--a need, a gap, a hole, that others can have the opportunity to fill, so that there can be unity, so that the whole body can grow up together into Christ. If everyone had surplus and no one had a lack, then there would be nothing to draw us together as a body. It is the flow of things within the body that binds it together.
Of course, there are other needs besides pecuniary ones and other gifts to give, some that don't make it onto anyone's asset lists at all and yet are the stuff life is made out of: friendship, example, comfort, a smile. Maybe stewardship as part of the body requires looking at both parts: Where do you have an abundance that you can share? Where do you have a lack that others can supply? Because I'm willing to bet we all have something in both columns.