This article from the Vancouver Province includes an interview with Gillis about what he's going to do about Burrows (as in: he'll trade him if he gets a buttload of high picks for him).
"Of course there are players who you don't want to trade but if someone offered you 10 first-round picks, would you do it? Of course you would," Gillis said. "Until you know the parameters of what's there, it's impossible to answer that question. When you try to talk in absolutes when you don't know the parameters, it's pretty foolish."
Well at least we know Gillis is not a Sith Lord. He doesn't deal in absolutes.
There are not going to be many teams who will piss away a lot of high picks, or even any high picks for that matter. It's not worth it anymore in the cap world. It looks like it could be mostly trades for players straight across or an influx into the waiver wire, like we saw today.
Who knows. I could be wrong.
At least we know Gillis isn't going to be a damned fool. He has the team's future in mind.