One of his first actions will be to try and implement a carbon tax, immediately alienating Alberta and Saskatchewan, which in the short term isn't bad politics for him, as he won't have much support in the prairies, and most of that will be in Manitoba. The real result of this will be increased pro-Western nationalism, which has always been simmering since his old man did so much to stoke the fires in the 70's and 80's. This will result in a slow down of the energy industry and be a net negative influence on the entire economy. The forecast tax revenue from the carbon tax will be less than projected, throwing the budget projections off, and the deficit will spiral.
The DND will feel the axe again, as the Liberals love to use the military as a whipping boy, even the shadowy remnant of a military that exists in Canada today. Veteran's Affairs will continue to be ignored by the gov't, unless there is a photo op involved. The Liberals will continue to send troops on "humanitarian" missions and the men and women will struggle heroically to achieve the goals of those missions, despite chronic supply and equipment shortages.
Healthcare will degrade as the federal government will attempt to off-load its share of healthcare costs to the provinces, who for the most part will struggle to maintain quality of care. Wait times will increase.
CPP payments will be cut and the collection age will be upped to 67 (possibly 70), as a short term measure to stave off the now retiring baby boomers and their demands on the system.
National unity will suffer: the West will see an increase in anti-Ontario & Quebec sentiment. The Maritimes will also see a rise, based on the impacts of the Carbon Tax on the east coast off shore oil & gas industry, unless Trudeau grants an exemption to off shore projects, which will ease the negativity in the Maritimes, but raise western alienation to record levels. Separatist movements coming to prominence in the West are a certainty, and a real possibility in the Maritimes, especially Newfoundland-Labrador. BC will continue as it has been: the lower mainland and Vancouver Island will support the Liberals but the interior and NE will not. Quebec will be mildly content as Trudeau will carry on with his father's appeasement strategy, which will not play well outside Quebec.
The Liberals will try to resurrect the National Firearms Registry, one more effort to pacify their urban base, while irritating the rural populations of the nation. Alan Rock will sponsour the resurrection bill from the Senate, where he will be appointed as part of the Liberal wave of appointees to reclaim the upper chamber.
The Liberals will be strong on anti-oil & gas legislation, stated as environmental regulations. They will give Aboriginal Affairs about the same level of attention as Veteran's Affairs (photo op or bust).
Will the country survive? Possibly but it won't look the same as before Trudeau took office.