As a lawyer, I often tell my non-lawyer friends we have two duties as citizens: to vote and to serve on a jury. Surely, if nothing else, our Republic was founded on the principle of an educated electorate that casts votes. But, if we ask for time off from our job to vote, we can be fired. See the case discussed by Russ Cawyer here. A three year employee asked to leave early to vote in the Presidential election in 2008 and was refused. She then left 15 minutes early and was fired.
In the decision, the Dallas court of appeals declined to create any new exceptions to the state at-will doctrine. So, the employee lost her appeal. In looking at these facts, one could argue that she was not fired for voting, but because she deliberately violated instructions from her supervisor. So, the facts are cloudy. But, in the end, we are "at-will" employees. We can be fired for taking time off to go vote.