In Saskatoon, every Tim's I tried accepts Debit. They don't accept Visa, for obvious reasons (the higher surcharge), but I've never even been given a second look with Debit. I've been to at least three or four different locations in the last couple weeks, and every one of them accepted it.
The ones in Edmonton on the UofA campus all accepted it when I graduated there (just over a year ago). Maybe not the one in the Student Union Building, because there are several stores there that don't, but the one in the Central Academic Building I'm pretty sure did, and the one in the Engineering Building absolutely did.
I haven't checked the ones here in Grande Prairie, but I know they did accept it recently. During my stay here I'm bound to make a trip or two past it, but I'd honestly be surprised if they ripped the Interac machines out of there.
What the company should do is have a Coffee Card thing, where you can pre-buy a $50 or $100 amount, and every time you visit they just swipe it off the card (no pin or anything, so its basically just like cash). Just like this Dexit thing (which I quite like the sounds of, I'd love to see it catch on everywhere), but have it available for use at every location in the country.