Ponzy,
Since you are in NJ, before coming out to contemplate Whitney, I would suggest taking a couple weekends and do some of the longer climbs in the Adirondacks which, depending on where you are in NJ, is 4-6hrs drive north.
Climbs such as Mount Haystack (5000+ft gain over 19 miles)-don't confuse this with Haystack Mountain which is smaller to the north, Nippletop/Colvin combo, Colvin/Blake/Indian head, Gothics/Armstrong combo, Both Wolf Jaws/Armstrong, Marcy/Phelps, all of which will be over 5000ft gain and 16-19 miles over Hard terrain. If you can do these and have gas left over at the end of the day, your legs will be ready for Whitney. Now you need to think about the elevation.
As others have said, you will need to develop your acclimatization strategy since on The Main trail, you'll be hiking at ~14,000+ft for over 5 miles once you reach Trail Crest and back. Think about this: Half Dome max's out @ less than 1000ft above the trailhead for Whitney.
You can eat a ham sandwich on the summit any east coast peak, but at 12,000 ft, you might only want a gel pack or candybar, so know what fuel your body can deal with. Also, come out to the Sierras a few days early and climb either Boundary Peak (13k) or even better, White Mountain 14.2k in the White Mountains - its only 15miles/+3000ft gain but will give you an idea of how your body responds to altitude.
You'll also lose a lot of elevation on the backside of Whitney so if you run into trouble, you won't be in a good spot, so make sure you know how your body functions at altitude after a long day out. Assume 12-18hrs for a day hike if you're not planning on camping. If it took you 12hrs to do Half Dome (from happy isles), it will take you more like 17+hrs on Whitney.
Good luck with your training!
