what will happen if i cancel my credit card to avoid paying non-refundable hotel?

I am an Au Pair from South Africa and I am 18 years old, staying in the US for a year and am planning to go to New York in December and stay for 12 nights. I've been looking at tons of hotels and have made 2 bookings that are not prepaid and have free cancellation. I accidentally booked a non-refundable hotel and after calling customer service like 5 minutes after booking, the hotel manager chose to follow hotel policy which is to pay the total amount if cancelled. This amount (incl. taxes) is over $1700 and with the pay I get I won't be able to make it because I still need to buy plane tickets and have spending money. The hotel is an hour out of NYC so paying $1700 is both impossible and not worth it. It is not prepaid so the hotel will only charge me at check-in. I wanted to know what would happen if I cancelled my debit card? Would the reservation be cancelled? What if I put a daily limit on my card, would the transaction be rejected? What if I just didn't have enough money in my account? (this would most likely be the case) Please I need help :(