Handling several acceptance letters from different schools If an institution tells you, look here is an admission offer, and you should let’s know if you accept it or reject it by the day after tomorrow. Meanwhile, you are still waiting for a word from other places that you applied to.

So, what is the most diplomatic and tactful way to communicate “Hey, I can not  accept/reject the current offer right now. That's because i am waiting to hear back from other schools, and I need time to decide upon that”? At the same time, I do not want to sound like careless about the offer.
It would be polite to let them know that you "won't be ready to make a decision before some date". Asking them to hold the offer open for a bit and requesting a reply. 

If they really insist, then you have to make a decision about acceptance, but they might not, unless they have an overabundance of candidates. But, going past their due date implies risk that the acceptance will be withdrawn. So, be prepared to make a decision on short notice. 

Letting the date pass without notifying them is probably your worst option, however.