The trick with my regime is to ensure you do different muscle groups after one another - this makes the cardio work, heart needs to be pumping the blood around your body,
eg:
upper chest, upper legs quads, upper back, stomach, shoulders, calfs, lower chest, stomach, biceps, upper legs hamstrings, triceps, lower back, calfs, shoulders then repeat until you hit 20 minutes - rest and then go for another 20 mins.
note - don't increase the weight during the work out, do it the next day if you feel you need to.

I'd say if you add a run later on say a quick pace 2 miles (rather than the eliptical trainer) you'll be laughing.

Give it a go! if not now try it as a change when you get bored or your body gets 'used to' the current regime you are doing.

Good luck

Just remember that your workout the day prior is burning up your store of glycogen, which is muscle fuel. However, the store is typically good for 12-18 hours, so a workout 24 hours prior to the event isn't as bad as a workout 12 hours prior. I experimented with this and found it to be true, 18 hours is enough time to top up the fuel stores, but 12 hours is a bit of a train to work through.

Remember to fuel your body properly with good carbs about 3-4 hours before the event, and then top up the tank just before you head out assuming the ride is two hours or longer. You can last 90 minutes before you truly deplete your glycogen (assuming a good pasta meal night before and fibrous carbs morning of), but two hours or more will require a bit more fuel, like a power bar or anything at 4:1 carbs:protein.

An interesting fact I read recently: Fruit carbs fuel your brain and "survival" organs, wheat/grain/rice carbs fuel your muscles. Any excess fruit carbs turns into fat (but not that much fat, but away from the muscles), and excess grain carbs go to fat. But it is interesting to note that fruits are the basis of survival whereas nuts, grains, and rice fuel the body.