That depends on the circumstances that surround your waking up:
If you've just woken up from a dream and are really groggy but aware that you've just woken up and can do a DEILD, then you'll be able to easily pull it off.
If you've woken up and haven't moved but aren't getting right back to sleep, don't give up - you'll miss 100% of the lucid attempts you don't make, so make the attempts, and don't lose heart if you start to get back to sleep and wake back up, keep attempting! I completed this month's advanced TotM after a few failed DEILD attempts one morning.
If you've woken up and already moved around some, your chances are very much decreased, but it's still possible to DEILD.

Whichever the above circumstances you find yourself in, give it an attempt, even if you think you're too far gone - you won't know til you're lucid again.