I have spent time as an attendant to a family member on more than a couple of occasions, for at least a fortnight or more each time, and am just recording my thoughts, in a random fashion.
When you are a caregiver, you often get offers like, "if you want help let us know". But how often does a caregiver remember your offer, especially when he or she is caught up with taking care of the patient? How does the caregiver know what kind of help you are willing to offer or whether you are reliable? The burden of providing you with opportunities to help can be too much for the caregiver, especially sitting in an ICU waiting room or a ward with a patient in pain. If you really want to help, show up, find out how you can ease the burden off the caregiver in little ways. And act. Often, you could be offering help just to satisfy your conscience or as a nicety. You move on, once the caregiver says, "Thanks. Will let you know." The caregiver doesn't know if you really want to help or you are just saying the standard line we all tend to use when we don't know what to say.
If your need to help is genuine, you will find ways to do so. If you are also caught up with stuff in your own life and can't offer help, please don't make false promises or offers that one can never count on. Honesty helps. I have not offered help to people on many occasions because I wasn't in a position to do so. Obviously we can't all help everyone all the time.
Most importantly, if you are not confident of handling any of this, don't just keep offering vague help and then saying, "but they refused. I offered."
Make up your mind on whether you want to help out or not, and when, and act accordingly. Your sincerity matters more than anything else.