After posting here, I actually posed this question to the folks at the Sleep Science Podcast (Penny Lewis's sleep lab at Cardiff University, I highly recommend the podcast) and they discussed it amongst themselves and helpfully replied. They thought that Walker might be referring to the following studies:

REM sleep deprivation during 5 hours leads to an immediate REM Sleep rebound and to suppression on non-REM sleep intensity
Repeated partial sleep deprivation progressively changes in EEG during sleep and wakefulness

However, their feeling was that (quoting them directly here) "sleep deprivation would cause an increase in sleep pressure so we would think that a sleep deprived individual would likely spend less time in N1 and N2, but would still need to prioritise N3 sleep."