There is lots to address here. Please forgive the length of this post.
1. If you check out my blogs below you'll see why you should never use Spark's figures for the elliptical. www.sparkpeople.com/mypage_public_journal_
So while Spark is best for walking/running type movements, never use their figures for magnetic resistance. Use the machine's, or if you want more accuracy buy and wear an HRM.
2. You should never out-exercise your goal. But you should not change your exercise! Change your goal! You can manually set how many calories to burn each week on the fitness goals page and you should do this and set it to be more realistic. It is the calories burned figure that is used to calculate your needs, not the calories tracked.
3. The "Weight Loss" program on this machine - does it keep you at a pretty low and easy pace? Many machines still promote the "fat burning zone" of lower intensity cardio to promote fat loss. This is a mistaken application of science, and isn't actually the best way to burn fat. The best way is to work hard - as hard as you can reasonably manage to do. If this routine leaves you feeling like you didn't work much, try ignoring the machine's recommendations and just putting the resistance up till you personally feel like "Boy, that's hard!"
It's better for fat loss to burn more total calories, not to burn a greater percentage of a lower total calorie value directly from fat. It doesn't matter what you burn in the exercise session - the body compensates the rest of the day to make up for it. So burn as much as you can! :)
4. Your goal is not feasible. The site allows all users to set up to 2lb/week, it isn't weight-based. But your body is weight-based. Bodies don't want to lose much per week, the less there is to lose.
I recommend a general guideline of 3% of what's left to lose each week. So you have 20lbs to lose in total, at the moment you should be aiming for 3% of 22 (0.66) pounds per week loss.
When you try to lose weight faster than the body wants to, the common result is that it rebels and doesn't lose anything. Slow loss is at least loss in the right direction!
I'd recommed keeping half a pound as a minimum due to the inexact nature of all the estimates in the equations anyway, so you really won't have long till you're at that, so you should probably set half a pound now as your goal. That would have those 22lbs gone by mid January 2014. Maybe set Christmas as your goal, push a little harder, and see how that goes.
But June? No. You're not fat enough to lose that much weight by then, sorry.
5. Last thing - no strength training? Strength training is great for every goal and in every body and will definitely help you to lose weight and make sure it's "fat" that you're losing, not muscle! :) Maybe do this routine M/W/F, with ST on T/T and a wildcard for either Sat or Sun, go do something fun outside! Play a sport, ride a bike, take a scenic walk, etc. :)