1) The person will be able to tell that your offer is phony. For example, you're really general and say something like, "Give me a shout-out about what you need." She may or may not accept your help, but either way she will think to herself, "What a lame friend."
2) If she accepts, you will keep thinking—despite knowing it's all your fault—"She is so demanding; this is too much for me." And she will sense this and think, "What a lame friend."
How much easier it would be to just skip all that and say outright, "I can't help, I'm sorry. And I don't want to lie about it and ruin our friendship."