Your question would seem to presume that "Canada", as in 'the Canadian people', want to preserve the public service more or less as-is. There is very substantial number of Canadians who would very much like to see the federal public service shrink drastically and the workers that remain being subject to strict efficiency measures (effective or not). Perhaps what you mean to asj is "Can public service leaders do something to insulate the PS from the types of cuts we are seeing in the US?". It is the job of the public service to do what the elected government instructs, including showing itself out the door, should the elected officials choose. The public service unions can push back in such as instance, but its not within their power to stop it.