Allow me to add my two cents, answering your original question as well as the one in your reply to Davi's excellent answer.
Yes, 'esse' works for both past and future times. 'Este' is just for the present, even if that present encompasses a little bit of the past in the speaker's view. For example:
'Não tinha feito muitas coisas esses últimos tempos, mas esta semana ando muito ocupado.'
('Esses' because it refers to a past time before the current situation of the speaker. Note the use of 'esta', because the speaker is talking about the current week.)
'Andei sumido estes tempos, mas hoje quero sair de casa.'
('Estes' because the speaker is still in 'these times'.)
'Vai ser difícil sair com os amigos esses tempos.'
('Esses' because it refers to the coming future.)
But that's the theory. You should learn that if you want to write grammatically correctly, though most Brazilian native speakers would probably overlook that and not pay attention to what word you've used. In practice, most Brazilians just say 'esse' and variations, as Davi pointed out, because it's easier to pronounce (one less sound!) and those rules don't naturally affect the meaning, so we'd probably just say 'essa semana' and 'esses tempos' in the examples above, most of the time.
When people write, however, many times they use the 'este' set of words when they should use the 'esse' one. That's called 'hypercorrection'. Since everyone uses 'esse' freely and perceive 'este' as formal, they end up using 'este' when they're not supposed to, thinking that you can just use it arbitrarily to sound more formal/grammatical. That is the case of that particular expression you've brought up: you may find some results of 'um dia destes' on Google, but I can't particularly think of a situation in which it'd be connected to the present; it either relates to the past ('um dia desses minha tia me reclamou!') or to the future ('um dia desses minha tia vai ter um enfarte!'), acting as a fixed phrase. Hope this helps!