6:54 p.m. on February 18, 2012 (EST)
Forget a well balanced diet that includes vegetables and protein. You want as many calories in you for those two days as you can get. Much of this will be from simple sugars and perhaps carbohydrates from pasta like things. You will be expending upwards to 600Kcal an hour (400 average) while going up hill with a backpack. You can do the numbers.
Leave the kitchen sink at home take enough to keep you warm and calorie loaded.
Stairs come to mind (along with a run/jog program - http://exrx.net/Aerobic/JogWalkProgram.html).
You will spend many hours in unrelenting uphill walking. Aerobic fitness will be your main goal. As WhoMeWorry has suggested, pick a constant cadence and don't cause yourself to be panting or needing to stop often.
Step/Breath method is an excellent way to get in shape but also to handle a long (11mile uphill) walk. The goal is to maintain your heart rate at a consistent steady rate (within reason). Somewhere around 80% of your maximum is sustainable for most who have spent time getting ready. One way to get close to this rate is to take on a LONG set of stairs or a long steep grade after a 15 minute warm up period, start a test run.
Inhale and put the right (or left) foot forward. Exhale when that same foot strikes again. In other words, you perform an respiration cycle for each right to right foot stride. Establish a rate of stepping and breathing that you can maintain for at least 15 minutes but that is somewhat uncomfortable to keep going. It definitely is not a stroll. That would be around 80% of max. This 'slower' rate allows you to exercise at a higher rate longer. You will probably find you are hungry. You need enough nourishment to keep up an exercise program. Eat well balanced equal sized calorie meals often, maybe 6-8 times a day and drink loads of water.
While hiking if you find you need more air take shorter steps, if you are not working at it hard enough, stretch out your stride. The trick is to establish a constant breathing rate that does not cause you to stop often. The longer you can maintain this level of effort the more 'fit' you are.
If you have to stop often you are maxing your body out. Do this too often and you will suffer the next day from the bad management of energy today.
Working out at a gym under some infrequent supervision from a trainer is worth the money spent - especially if you can get somebody who loves/cares for you and is willing to get a membership and a few hours from the staff. Tell them you want 75% of the time on the muscles below your belly button and the rest above it. Pumping iron (or the equivalent on machines) brings surprising advantages to hiking and well worth the extra time/effort. Plan on every other day at the gym working different sets of muscles every other time. This allows the muscles time to recover.
Leave extraordinarily early from the parking lot. You will hopefully get an earlier start than most of the army of hikers who will be on the trail with you. It also gets you a better camping site as high up as you can get the first day. Rest eat and drink lots the rest of the day
Start getting used to drinking more water than you think is ever needed to keep your body going. By the time you are thirsty at altitude, you are already dehydrated.
If you make it a two day trip leave even earlier the next day... perhaps midnightish. You want to beat most of the crowd to the handrails/cables/switchbacks AND be off the top before noon, to beat any storms and certainly before the lightning starts up there.
Be sure you take rain/wind jacket and 200 Polartek equivalent fleece to the top with you. Slather on the UV lotion and lip protection so you don't end up a crispy critter and wear a brimmed hat that will not be blown off and many miles away.
It is a trip of a lifetime, beautiful and exceedingly rewarding.
Aside: If you are susceptible to altitude problems, you might consider a day hike of Whitney getting back to lower altitude before the body catches on it is up too high. At any rate, if you get ill because of altitude, don't try to tough it out just to get to the top. The risk is too high for the bragging rights of the summit. Next time plan on taking longer to acclimatize and get some pharmacy help.