In order to stop this, he sends an operative back in time (through the use of a top secret project) in order to inoculate Heinlein on the Roper so he wouldn't get sick, and wouldn't write his sci-fi.
After the operative returns and reports success, they realize that the space program hasn't been destroyed, but has been strengthened a thousandfold. Orbital colonies, lunar colonies, and heading towards Mars and beyond.
Turns out that without the illness, now Admiral Heinlein stayed in the Navy, and used his imagination and pull to start a space program much earlier than originally, and continued the push into space.
I wish I could remember who wrote it, and the name of it, but I thought it was an excellent story.
I believe it was either written or anthologized by Spider Robinson. The "operative" was none other than William Proxmire (he of "Golden Fleece Award" infamy). Proxmire hated the space program--it took bucks away from his beloved social(ist) programs.
It was written by Larry Niven, but I cannot remember the title. He even got Heinlein's permission before writing the story.