4 days is doable if you condition and pack smart. I did a 7 Day trip last year sans conditioning, with a hefty pack and we made Whitney on day 5 (hiking out that day would have been easy).
If you're looking for 4 days, I would shoot for this itinerary:
Day 1: Onion Valley - Kearsarge - Bubbs Creek Bear Box #2 (11-12 mi)
Day 2: BCBB #2 - Forester - Tyndall Creek (w/ Bear Box) (10 mi)
Day 3: TC - Guitar Lake (10 mi)
Day 4: GL- Whitney - Out (16 mi)
Thanks, that's basically what I had planned out:
Day 1 - East Coast to West Coast Travel
Fly from Boston (most likely) to either SoCal or Las Vegas
Drive to Eastern Sierra (4-6 hrs of driving)
Day 2 - Hike Onion Valley to Vidette Meadow
8.7 miles || +2700, -2200
Day 3 - Hike Vidette M. to Tyndall Creek
12.4 miles || +3600, -2200
Day 4 - Tyndall Cr. to Guitar Lake
11.1 miles || +2400, -1400
Day 5 - Guitar Lake to Whitney Portal
15.5 miles || +3305, -6445 || -3140 net elevation gain || 12 hours
I was thinking the first day would be a little shorter because we need to pick up permits that morning most likely.