A significant portion of my backyard is dirt, and needs to be seeded. Is it too early to put grass seed down now (mid March)? When is the ideal time to seed in New Jersey?
The ideal time to seed in NJ is actually in the fall.
I recommend calling your local County Extension Office/ Master Gardeners; they will have plenty of information for you on this topic, including how to prepare the soil and how to choose the best seed based on your location, the amount of traffic the lawn will bear, and how much maintenance you are willing to put into it. There are new seed varieties out that require less fertilizer and less mowing.
They will also do a free pH test if you take in a small soil sample. A complete soil analysis at the Rutgers Soil Lab is $15 and you can buy your kit at the Extension office.
Here's a link that may be helpful.
What county are you in? I believe there are some programs around the state, sponsored by the Rutgers Cooperative Extension/Master Gardeners, on starting and maintaing lawns.
Here is a link that might be useful: Rutgers Lawn & Garden FAQ page
Fall may be best but anytime after the ground thaws out, The grass seed must be not dry out. water daily unless it rains, enough to keep it damp. It can take 14 to 21 days to see your results. Good Luck