First, everybody should read this:
King-Byng Affair - Wikipedia, the free encyclopedia
It's the nearest thing to a precedent there is for this situation.
It looks very likely that Harper is going to ask the G-G to prorogue (fancy word for adjourn) the House until some time in late January so the impending confidence vote will die on the order paper. He's promised a budget for January 27th, so presumably the House would reconvene shortly before that, then the confidence vote will be on the budget rather than the incendiary document the government introduced last week.
I doubt very much he'd ask for dissolution, that would mean an election, and with a coalition deal already in place and having had an election less than two months ago, I think the G-G would be constrained to deny such a request and ask the Liberals to try to form a government. Normally she'd be constrained to deny a request to prorogue the House too, when the session is less than two weeks old and the only reason to do it is to duck the confidence vote. But it's complicated by the presence of a band of separatists having the balance of power in the coalition. The coalition deal expires 30 June 2011, about 30 months from now, but the Bloc has agreed to support the coalition on confidence matters only for 18 months, so odds are we'll be having an election in 19 months anyway. And there's a great deal of rancour being expressed over the influence of separatists in the federal government, which is really the ugliest part of this.
Harper's arrogant folly has put the G-G into a very awkward position: no matter what he asks for and no matter what she decides, there will be bitter recriminations from one side or the other, which is not something you should do to the G-G. It's the influence of separatists in the coalition that's the real sticking point. If the Liberals and NDP had enough seats together to form a majority it's a no brainer: deny whatever Harper asks for, either prorogation or dissolution, which would require him to resign, and opt for the coalition. It's the separatist presence that might lead the G-G to opt for proroguing the House.
Predictably, almost everybody who objects to the coalition--including the Conservatives--doesn't seem to understand parliamentary democracy. We did not elect a Conservative minority government, we elected a House of Commons, the government is formed from within it by Parliament's internal rules and procedures and traditions, and what Dion and Layton and Duceppe have done is perfectly legitimate in that context. It's just those Bloc heads that complicate it. Note, however, that they have no formal role in the coalition, merely an agreement to support it on confidence matters for a period of 18 months, so we'll probably be having an election in 19 months anyway.
If I were the G-G, I'd say no to whatever Harper advises: meet the House next Monday and face the consequences of your arrogant folly, or resign now and I'll ask Dion to try to form a government. I wouldn't prorogue the House just to save his butt for another 2 months or so, while we all suffer through a period of media saturation with political spin and lying and name calling and ugly attack ads, nor would I dissolve the House and force an election nobody wants.