I think a not too high threshhold of space capability is needed to maintain MAD (mutually assured destruction) level deterrence.
You send out some 100-1000 ton launcher vehicles.
They go and hide on the non-earth facing side of an asteroid of which there are billions. They place solar energy collector around and then load up on energy. Telescopes are used to look for steerable comets / right composition / right size etc...
Launcher can either take material in space and accelerate it around Jupiter / Sun and then into the earth. 100km/s-1000km/s should be doable OR find the biggest steerable comet that can be nudged onto earth collision course.
Even strong nanotech enabled power would have a tough time finding the vehicles of that size that are actively hiding and built for stealth. Our current capability is that at large distances (30-50 astronomical units) we have just discovered a planet larger than Pluto.
Once the kinetic objects are on the way... a nanotech power would not be able to do much about the objects as they rounded the Sun. Objects can also not use that solar gravity boost. Tough to spot. tough to stop after spotting. Some active dodging of counter measures and active steering to course correct for attempts to nudge off course. It would take about 1 day to get from the sun to earth at 1000km/s
For the thinking on maximum destruction for deterrence, bigger objects (more tonnage) and fast (100km/s) but not super fast speeds probably works out best. At superfast speeds the object would become gamma radiation or cosmic rays at it hit the atmosphere.
For MAD, steering the dinosaur killers or near dinosaur killers would be tough to stop. If you take the long view and truck out years out to the Oort comet cloud and then start nudging the right object ... it would be tough to detect until it got far closer by which time it is orders of magnitude tougher to stop or deflect. The attacker has a big (many orders of magnitude) advantage. Picking the objects and direction and type of attack. Having first mover advantage to get things moving which takes less energy over longer time. The defender has less time and needs to be able to put more energy at stopping and deflecting. Physics works against the defender big-time.
the good news is that although this is first strike capability...if more than one side has advanced space flight...then it is relatively easy to maintain second strike capability. This means one does not have to race to attack first, knowing that if you are wiped out in a first strike you have deep space capability to destroy the attacker.