What exactly does get immigration under control actually mean? Have you thought that idea through carefully and deliberately? Or is this just another talking head segment you saw in the bar while downing a pint?
As others already pointed out, we rely on immigration to keep the work force going chiefly because of the declining birth rate. This applies for all of the Western world and we basically have a de-facto 1-child policy like China. The contributing factors are a different, but the problems are the same: a declining workforce, aging population and people having fewer kids or not at all.
Halting immigration entirely is a bad idea because it will very difficult to get it going again. I again point to China's 1-child policy, which was significantly worse because the Chinese favored male over female children. Further, they were either abonding or aborting female babies. So now there's a lot more males than females, which magnifies the problem. You can't make babies without enough women to go around.
We're definitely not going to solve the so-called labour shortages by halting immigration. We can't build housing and other infrastructure if the work force is shrinking where more people retire vs get hired. On the other hand, protectionism in some industries is part of the problem too. I don't think the unions actually want to solve the labour shortage because they want to keep competition out and wages high. We've been down that road before. I think another potential cause of this labour shortage is that Canadian kids don't want to go into the skilled trades. We have a supply side problem of people on multiple fronts.