"It then becomes your job to help the entrepreneur find a reasonable solution which is merely hard and gets most of what they wanted."
Many startups are founded by doing something impossible (Google, Apple, Akamai, YouTube, PayPal). Most of the remainder are founded by doing something useless (Twitter, Facebook, del.icio.us, Reddit, etc.) This is for very good reason. If something is neither useless nor impossible, it's quite probable that there's a big company out there that's already working on it, and they can bring more resources to bear than you can.
So if you are the entrepreneur and not merely working for him, it's your job to do the impossible. And yeah, that means turning it into the merely hard and then doing it. But if you aim for "merely hard" to begin with, you'll probably end up producing a mediocre product in the end. After all, products never have quite the same glamor when they're done as when they're conceived in your head.