Things It Took Me Way Too Long to Learn
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."