Frank,

Deer do not carry Borrelia burgdorferi. However, they have an important role in that they are where the adult ticks feed to engorgement and then reproduce, up to 4000 eggs per female tick! So the deer amplify the tick population. As the article states, the small mammals like mice and chipmunks are potent reservoirs of the infection, and so the tick larvae feeding on them amplifies the number of disease carrying ticks — up to 70% in some parts of New England!

In some parts of the country where the black-legged tick can be found in abundance, the infection rate with Borrelia is very low. In some of these places there are animals, like lizards, that actually eliminate the bacteria when infected ticks feed on them. So, they de-amplify the disease.

Regarding why some animals get sick and others do not, that is a matter of host susceptibility. In the animal world, dogs and horses can get severe Lyme disease, but sometimes with different symptoms.