Just how long will that eagle sit on those eggs?

Here is some information about how long an eagle will incubate their eggs for;

Incubating Eggs: 35 days
As soon as the first egg is laid, the female and the male take turns incubating. Both male and female eagles form a brood patch--a bare spot on their tummy where they can press their hot skin directly against the eggs or chicks to keep them warm. The female's brood patch is a little bigger and more feather-free than the male's. And the female incubates the eggs more often than the male does.

One study showed that the female was responsible for 72% of the incubation. (How much was the male responsible for?)

Eagles sit on their eggs most of the time--one study showed that the eggs were incubated 98% of the time! But when the temperature is warm and there is little wind, the parents incubate less often. Sometimes when the parents leave the eggs, they cover them with feathers and nesting materials. Scientists don't know for sure whether they do this to keep the eggs warm or to hide the eggs so predators don't steal them.

Eagles have VERY sharp claws on their powerful talons. When the incubating parent is moving about the nest, it often clenches its talons so the sharp claws can't hurt the eggs or babies by accident. The parents are also very careful to step around the eggs to avoid crushing them. Parents probably turn the eggs at least once a day, but scientists aren't sure how often this happens or which parent does it.
Source:http://www.learner.org/jnorth/tm/eagle/NestingPhenology.html