Would more people be organ donors if there was a good tax break for it?

Year after year it is said how many people need a transplant for this or that but the list is so long and the donors so scarce. If for each year a person was a registered organ donor they could shave 10% off their tax liability or get a flat tax cut of $3,000 for instance, would not more people think about being donors if they qualified, we know not everyone who wants to be a donor could?