Plus the launch plume from the pad... and the UAVs and satellites giving mid-course guidance... There's a ton of targets to hit.
We don't have any launch phase defensive systems in place (yet), and it wouldn't be feasible to whack their satellites to prevent guidance updates given the short warning time we'd have (I'd also rule out jamming the satellite signal, since an encrypted focused microwave beam would be nearly impossible to detect, let alone jam). Of course, we could take out their birds proactively, but by that time the shooting war would be in full swing, and I hate to even think about that.

You do make a good point though. Against a moving target, unless this thing is nuclear-tipped, it must have terminal guidance. This means the seeker must have a protective heat shroud, which has to be jettisoned before it can start scanning for the target. That should increase the radar cross-section enough to allow detection, but your defensive systems would have to respond quickly.
What really sounds daunting would be a low-observable UAV using laser ranging to get precise target position which it then uplinks via satellite for secure tranmission to the weapon. That would make the weapon purely passive and
extremely dangerous. In that case, you damn well better make sure your surrounding airspace is clear.