Yes, but even.... Ottawa runs the EI program. It has its own tiny version of active labour market policies and training initiatives. Some of that's been farmed out, more and more, to the provinces. But this is clearly an area of overlapping jurisdiction.
Now, whether you can build a consensus with the provinces.... And maybe you have to have some asymmetric federalism; you get the ones you can at the table to talk about employment levels, wage levels, and what to do about them. I think you could get more of a political legitimacy for that kind of issue, even from the middle class, than you would if you were to call it a poverty reduction strategy.