I would say that three weeks is the minimum time you need for this trip in order to have some time to play along the way. This would give you 7 days to play and 14 days to travel. I'm not sure it would be worth it.

If your only intention is to "bag" places to visit in order to say you've been there...even though you are only driving through, then you can do it in 14 days. If you want to do a whistle-stop tour, meaning you have time to stop for a quick visits at some places along the way but aren't taking time for any in-depth exploration or planning on doing much relaxing/playing, then 21 days will do it. And if you're happy making this trip under those conditions, go for it.

I just don't think you're being realistic. It sounds like time and budget are issues. On this type of trip, gas is going to be your biggest expense and the one you have most control over. So why not actually plan a trip that is feasible in 14 days and that fits your budget?

From New Jersey, you have several options for more regional trips that will cover less miles and, consequentially, keep that gas bill down. How about a swing up to Maine, maybe return via Montreal and Toronto? Or the various Atlantic beaches? Or Chicago? Or Memphis area? You have a ton of options that would be cheaper because you're not driving so far.

This post should give you some good money-saving ideas. At the top of that post is a link to another post with the steps you'll need to go through to determine your budget. Why don't you work up a preliminary budget and then post it here so we can help you figure out if it is reasonable?

Expect gas prices to hike in the summer. They always do.