From Longman Dictionary of Contemporary Englishsleep on itsleep on itspokenDECIDE# to not make a decision about something important until the next day → sleep
Examples from the Corpus
sleep on it• He asked if he could sleep on it.• We decided to sleep on it.• With so much within easy reach, we were clearly spoilt for choice and decided to sleep on it.• There's no obligation to do anything at all. Sleep on it, and tell me what you think in the morning. 