Sending humans to other star systems is not feasible with current technology. So to imagine it you have to assume some kinds of technical advances.
Nonsense!
From the surface of the earth to a low earth orbit to a solar escape orbit is 17 kilometers per second delta-V.
Assuming a top of the line hydrogen/oxygen rocket with a specific impulse of 4,500 m/s exhaust velocity, the Tsiolkovsky rocket equation tells us we require a fuel fraction somewhat in excess of 99.99% to fling ye spacefaring gent where no man has ever gone before. Since staging can give us effectively arbitrary fuel fractions, this is quite doable.
Now, as for keeping the poor bloke alive, well, you ever did mandate life support.
The problem I have is that we have no way of actually containing a nuclear blast. Steel or aluminum just won't cut it. The whole idea won't get off the theoretical drawing board until there is some manner of containing and directing the explosions.
Diamonds or graphite. There is no fluid medium with which to transmit a blast wave, so all the pusher plate need to be able to do is survive the incident radiation and impulse of incident vaporized bomb debris. A little active cooling, a little ablation, and you're good. Since all that vaporized junk just did smack into you, you go the other direction (conservation of momentum and all that).
Easy.
Ish.
Now, if you want a little bit more specific impulse, you use a big (several kilometers big) fullerene parachute and detonate the bomb in between you and the canopy. The net force will be away from the open end of the parachute, and you will harvest a higher percentage of the blast energy. Moreover, you're using a tension structure, which should have less mass.
