This brings up a couple of points.
How many of our first responders actually have a radiation detector, and know how to use it? Police, paramedics, fire crews? I doubt that many of these units have a device that can measure radiation. So in the event of an incident with a serious radiation threat, the Gov't would need to bring in special teams. They certainly do have such teams - but i'm not sure there is any system to transfer the info to the public. The result is likely to produce a lot of confusion and fear.
Pete
Can't say for the US, but in the Netherlands, every fire engine has a radiation meter.