There's quite an exhaustive takedown of this claim by biologist P.Z. Myers on his blog Pharyungula.

The paper he relies on is

Calabrese EJ (2008) Hormesis: Why it is important to toxicology and toxicologists. Environmental Toxicology and Chemistry 27(7):1451-1474.

While the effect of hormesis is real:

Hormesis refers to a biphasic dose response curve. That is, when exposed to a toxic agent at very low doses, you may observe an initial reduction in deleterious effects; as the dose is increased, you begin to see a dose-dependent increase in the effects. The most likely mechanism is an upregulation of cellular defenses that overcompensates for the damage the agent is doing. This is real (I told you there's a grain of truth to what she wrote), and it's been observed in multiple situations.

However, there is one important caveat: (my emphasis)

However, the key thing to note about hormetic effects is that they only apply at low dosages. Low dosages tend to be where the damaging effects are weakest, anyway, and where the data are also the poorest. The US government recommendations for radiation exposure are based on a linear no threshold model in which there is no hormesis to reduced effects at low concentrations for a couple of reasons. One is methodological. The data we can get from high exposures to toxic agents tends to be much more robust and consistent, and we do see simple relationships like a ten-fold increase in dose produces a ten-fold increase in effect, whereas at low doses, where the effects are much weaker, variability adds so much noise to the measurements that it may be difficult to get a repeatable and consistent relationship. So the strategy is to determine the relationships at high doses and extrapolate backwards.

As a consequence:

In the low dosage regime, these responses get complicated at the same time the data gets harder to collect. This is why it's a bad idea to base public policy on the weakest information.

He continues to give a very simple example explaining the idea behind hormesis, before coming to his damning conclusion:

Here in Minnesota in the winter we get very snowy, icy conditions. If I'm driving down the road and I sense a slippery patch, what I will immediately do is become more alert, slow down, and drive more carefully — I will effectively reduce my risk of an accident on that road because I detected ice. This does not in any way imply that ice reduces traffic accidents. Again, with the way Ann Coulter's mind works, she'd argue that what we ought to do to encourage more responsible driving is to send trucks out before a storm to hose the roads down with water instead of salt.

 

Ann Coulter is blithely ignoring competent scientists' informed recommendations to promote a dangerous complacency in the face of a radiation hazard. She's using a childish, lazy interpretation of a complex phenomenon to tell people lies.

There's quite an exhaustive takedown of this claim by biologist P.Z. Myers on his blog Pharyungula.

The paper he relies on is

Calabrese EJ (2008) Hormesis: Why it is important to toxicology and toxicologists. Environmental Toxicology and Chemistry 27(7):1451-1474.

While the effect of hormesis is real:

Hormesis refers to a biphasic dose response curve. That is, when exposed to a toxic agent at very low doses, you may observe an initial reduction in deleterious effects; as the dose is increased, you begin to see a dose-dependent increase in the effects. The most likely mechanism is an upregulation of cellular defenses that overcompensates for the damage the agent is doing. This is real (I told you there's a grain of truth to what she wrote), and it's been observed in multiple situations.

However, there is one important caveat: (my emphasis)

However, the key thing to note about hormetic effects is that they only apply at low dosages. Low dosages tend to be where the damaging effects are weakest, anyway, and where the data are also the poorest. The US government recommendations for radiation exposure are based on a linear no threshold model in which there is no hormesis to reduced effects at low concentrations for a couple of reasons. One is methodological. The data we can get from high exposures to toxic agents tends to be much more robust and consistent, and we do see simple relationships like a ten-fold increase in dose produces a ten-fold increase in effect, whereas at low doses, where the effects are much weaker, variability adds so much noise to the measurements that it may be difficult to get a repeatable and consistent relationship. So the strategy is to determine the relationships at high doses and extrapolate backwards.

As a consequence:

In the low dosage regime, these responses get complicated at the same time the data gets harder to collect. This is why it's a bad idea to base public policy on the weakest information.

He continues to give a very simple example explaining the idea behind hormesis, before coming to his damning conclusion:

Here in Minnesota in the winter we get very snowy, icy conditions. If I'm driving down the road and I sense a slippery patch, what I will immediately do is become more alert, slow down, and drive more carefully — I will effectively reduce my risk of an accident on that road because I detected ice. This does not in any way imply that ice reduces traffic accidents. Again, with the way Ann Coulter's mind works, she'd argue that what we ought to do to encourage more responsible driving is to send trucks out before a storm to hose the roads down with water instead of salt.

Ann Coulter is blithely ignoring competent scientists' informed recommendations to promote a dangerous complacency in the face of a radiation hazard. She's using a childish, lazy interpretation of a complex phenomenon to tell people lies.