Sounds as though you are on two separate tickets. In that case you are somewhat at the mercy of the airline because of the separate itineraries.

As such, no you can not ask for the airline to pay for the hotel. The fact that they offered to put you on a flight the next day is because the change was more than 2 hours which is the cutoff for making changes at your suggestion. That is if the change is more than two hours you can typically make whatever change that works best for you, including a refund.

Unless there is another carrier that can get you there the same day I would say get a cheap hotel near the airport, enjoy the evening, and a nights sleep.