Blaming immigrants is easy because you get an immediate base amongst racists (the immoral). They'll perk up at the sound of your dog whistles, and immediately start barking shit like "finally someone had the bravery to say what we're all thinking". That amplification of your message then reaches the reactionaries, who accurately look around at the world that is hell bent on destroying them, but are a little too dense to understand the web of systems that make up that world, and thus are eager for a simple explanation (the stupid). And once your message gets embedded in the zeitgeist from that lot, normal, relatively detached from politics people start hearing all this talk about immigration being a problem, and believe it (the wrong).
The same way you can't be frugal to make up for making poverty wages, you can't shrink the pool of disadvantaged workers to make them advantaged.