It'll work when someone shows it working. Until then it's just conjecture.
This technology is not a matter of 'is it possible?' but 'is it technically feasible?' And the scientific community has been chipping away at the latter for a long time.
I'm not saying it's a valid goal - just until the technology is useful, it's not yet viable.
Compare to unified field theory, the Higgs boson and string theory.
A pessimist is an experienced optimist :)
http://en.wikipedia.org/wiki/Sun#Core
The Sun is not like a nuclear bomb going off. It's just a big radiating compost heap. Its huge energy output is due to its large size, and not the intensity of its reaction. (If the Sun's reaction were like a nuclear bomb, the solar system would be destroyed in a supernova-like explosion.)
In other words, nuclear fusion at the Sun's scale isn't very intense a reaction. Why do we expect it's a good idea for a power plant? Do we expect to get significantly hotter than a star? Significantly more dense? It makes sense how nuclear power works. Fusion power, it's not so clear.
Of course, there are fusion bombs as well, but aren't those set off by nuclear bombs?
What the "blanket" does at this point is exert pressure on the "core", which would be beginning to blow apart in a conventional nuclear device. Keeping the "core" together for just that small bit of time longer allows it to remain supercritical for just that small bit of time longer, with the energy release growing exponentially with a time constant of 10^-7 seconds.
where, as the diagram shows, fission comes up from the heavier elements (less energy difference) and fusion from the lighter (greatly more).