The plan calls for a craft weighing 20 tons. That's within the carrying capacity of several different lifters we have at the moment, I'm pretty sure.
With nukes, you're taking a gamble with much more complicated equipment. A nuke isn't just a lump of explosive and fuses, it needs highly sophisticated triggering electronics. And getting it there requires just as much sophistication as getting the gravity tractor there.
You know, people did think this through before publishing the idea.