I haven't signed the "Resign" petition. (Shock! Horror!)
That is not, in fact, because of any respect for him left over from his first term as Chancellor. He does not deserve to be running the government.
But what does it mean to ask him to resign? Either we (a) get another non-entity machine politician from the Labour front bench, or (b) we get a general election where presumably Cameron gets in.
I'm not at all happy with the constitution we have, but having governments chased out of power as soon as they lose the confidence of the media is not likely to improve it. The ousting of Brown would not be a victory in any sense - it would be the psychological substitute for a victory.
If there's any coherency to my present political position, it is a rejection of psychological substitutes for victory. That is why I can be an activist for the Libertarian Party UK while my guru Mencius writes about "the fundamental comedy of democratic libertarianism - a proposition no less grimly hilarious for its infinite boneheadedness." Being unsatisfied not just with Tony Blair but also with Gordon Brown, and also with the Labour Party, and also with the Conservative Party, are steps on the road to being unsatisfied with our democracy. Future steps to guide my comrades through are being dissatisfied with democracy itself. I don't, of course, need a majority to go through this process, but whatever can be done in the end, I'm not likely to do it on my own.
So, if you want to take the system at its word, vote LPUK. After that fails, come with me and Menc....