The risks of organ donation

Hell is excluded from this discussion.
Play nice.

It is sometimes said that organs will be taken earlier than they should, and that doctors won’t try as hard to save patients, if someone else needs their organs.
Some people feel that being a donor could mean that they won’t try as hard to save you.

Is there any evidence of this?
Are there any cases where this has been identified?

Cecil Adams on organ harvests.