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)