The FAQ on this is a bit confusing. The wording on continental.com is:
The same-day flight change option will be available within 24 hours before your original scheduled flight. Inside of this timeframe, you can try to take an alternate flight so long as it departs no more than 12 hours from when you are making the request.
But this doesn't make much sense. It appears to be saying that if your flight departs at say 3pm tomorrow, and you are looking to make a change at 3pm today, you can't switch to a flight that departs at 1pm tomorrow (because it's 22 hours after you're making the request).
Why not just have it so that within 24 hours of your original flight, you can stand by for any flight that leaves within 12 hours (forward or backward) of your original flight?