The movie Deep Impact involved an Orion style spaceship built in orbit. The major implausibility in that movie was they were able to build it in 2 years, in secret.
OK, one of the major implausibilities.
Well, given enough funding, they probably could do it in two years, and the secrecy actually wouldn’t be too hard, if you painted all the parts matte black before launching them. At worst, folks would figure out that you’re building something, but they wouldn’t know what.
It’d be possible to assemble the spacecraft is orbit, but those steel/tungsten shields would be impossible to launch whole. It’d be hard as hell to weld those in space with anything approaching the quality you’d need. And I sure wouldn’t want to depend on a bolted structure as protection from a nuclear blast.
Seems to me the only fuel usable is antimatter although calling it off the shelf technology is pushing it a bit. While there is some antimatter sitting at Fermi Lab just outside Chicago as well as a variety of other accelerators they don’t have very much. IIRC someone said that if we increased antimatter production 1,000x over today’s levels it’d take several hundred years to get enough together to launch the space shuttle.
However, the good part about antimatter is it goes a LONG way in comparison to its mass. Again, this is dug out of a dim memory, but I believe I heard that about 1 ounce would be sufficient to launch the space shuttle into orbit.
Why? I never let it stop me before. 
In fact I had lunch just today with Lady Deirdre Sky, at Gaia’s Landing, on Chiron.
Well, fogmage, you can tell her that if she dosn’t get away from Mount Planet, I’m going to fed-ex her a planet-buster. 
Why did those smug Gaiens get to be the “default” faction, anyway?
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“Brought to you by Vermont. The other, smaller Wisconson.”
A very good summary of the history and technology of the Orion project can be found at Project Orion.
What is interesting is that most of the problems involved with pulse-nuclear bomb propulsion seem to have been solved, and this was back in the 1960’s! We could almost certainly build an orion ship now. We could even build a really big one down here and launch it in mid-pacific - dirty, but no worse than a big nuclear test.
Pigs in Space - check out the “small Orion” story, a ship which could be launched using three Saturn V’s. It included a small (33 ft) pusher plate. The small size of this plate cut the specific impulse dreadfully, but it could be done.
“It’d be hard as hell to weld those in space with anything approaching the quality you’d need.”
Agreed, using terrestial welding technology. But if we want to develop any kind of infrastructure in space, we’d damned well better learn how to do this! Maybe you could plasma-ablate the pieces you wanted to weld to give a clean, extremely reactive surface (it’s a GOOD vacuum up there) and bang them into each other. Or maybe we could use a variation on friction or diffusional welding - you don’t need to have a liquid phase to get a good weld.
Sure, but wasn’t the idea to use today’s technology? And keep in mind, with regard to welds, you have to be able to do it consistently, with no voids, and you’d have to be able to inspect all of it, too. I’m not saying it can’t be done, just that there would be a long development and testing process, before you can even really design the hardware.