To estimate this order of magnitude. A typical (non MERV) 1.2Mt B83 in the active US nuclear arsenal would likely vaporize ~100m diameter hemisphere to deflect

To estimate this order of magnitude. A typical (non MERV) 1.2Mt B83 in the active US nuclear arsenal would likely vaporize ~100m diameter hemisphere to deflect a relatively large 3km asteroid. Assuming an asteroid at 1-10 km/sec relative velocity 12 days out is 1-10M km away and earth is ~10k km across. So a deflection angle of ~1-10mrad is needed for a 3km (~10km3) spherical asteroid mass of ~10^13kg. A 5E15 J/Mt 1000kg bomb with a half momentum of about 10^9 kgkm/sec could deflect an angle of 0.1mrad 12 days out. Half energy conservation would gives you a similar ~0.01km/sec dV, so you'd need >10x more time or >10x more 1Mt nukes for a 3km asteroid. It gets much worse for larger asteroids, but interestingly dV doesn't change quickly with relative velocity since the required angle falls as the velocity rises.