Unfortunately I am in a similar situation.
Family Friendly Jury Duty website:
http://www.familyfriendlyjuryduty.org/ has summaries of the state laws, and of some of the laws that were proposed, but didn't pass.
Even in a state with no jury duty exemption for nursing mothers or other caregivers, some districts may have a formal or informal policy of allowing postponements or excusals. It can't hurt to ask.
Generally, you write a letter requesting postponement, and outlining the reasons why. I would start with a letter rather than a phone call, to fully lay out the fundamental issues of why jury duty is difficult for you at this time. Mention that if you serve, you will require breaks for nursing or pumping, and how frequently. The physical symbiosis between mother and nursling is something that many people don't understand. In my letter, I took the slant that arranging breaks and a place to pump was a necessary accommodation that would also be an inconvenience for the court, and it would be better all around if they would just allow me to postpone (again).
