sleep on it字面意思睡在上面，引申为好好考虑一夜 ；考虑一晚上。

【例句】
Let's just sleep on it. And after a good night's sleep, we can make up our minds and go buy it after work.
让我们今天晚上考虑一下，睡个好觉以后，我们可以再作出决定，下班以后再去买就行了。

Could I sleep on it and let you know tomorrow?
能不能让我晚上考虑考虑，明天答复你？