I agree with 'pj', and would go even further to say that as a seller you really shouldn't ever request a cancellation -- you will just be creating an upset buyer who will still be able to leave FB/DSRs on the transaction. Let buyers ask you first (which usually means they're happy to get out of the transaction and you'll have no issues to deal with).
However in your particular case, if you still had the item available but the buyer wasn't paying within a reasonable time, then the best course would have been to open an Unpaid Item Case in the first place. Likely the reason you can't do that now (or at least not immediately after requesting a cancellation) is because, if you think about it, the two requests are contradictory -- you wanted to cancel the transaction, but now you'd be telling eBay you want to be paid after all.
If you were trying to cancel the transaction for reasons other than a damaged or otherwise unavailable item, then I'd suggest, rather than attempting to relist the item (which you may find you're prevented from doing anyway because the buyer has refused to cancel), wait about 4 days and see if you're able to process the Unpaid Item Dispute. My guess is that the buyer's cancellation might have had the effect of "re-starting" the transaction, and perhaps eBay gives buyers a few days to make payment (as if it were a new transaction), blocking sellers' ability to file an immediate UIC.
The problem is that you haven't got a lot of time to deal with this if the item sold around Jan. 6th. You could try to phone eBay customer service and explain the situation (emphasize the date the buyer purchased, that he/she has never paid and that you made a mistake in asking for a cancellation). They may permit you to file an Unpaid Item Case.
If you think about it, there shouldn't normally be any reason for a seller to request a cancellation if the buyer isn't asking for it. In my view, in the rare instance where a buyer has purchased an item (but not yet paid) and the seller finds she/he can't go through with the transaction for a truly valid reason (for example if the item is suddenly damaged), then the seller is in the dilemma of not being able to produce what was promised.
What do regular stores do in this situation? They give you a rain check, they give you a consolation discount coupon, or they send you a free item of similar value -- and you might agree to forget about the original transaction. In any event, they usually apologize and offer some sort of compensation. Something to consider.
I was once in a similar situation when a purchaser bought a sewing pattern that was actually out of stock (I had shown the wrong quantity in my listing). I apologized profusely and promised to send her that pattern once it was reprinted, completely free of charge, which I did. Six months later, the buyer returned to make other purchases.
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