I don't think it's up to the working class to accept or reject policies of any meaningful impact (or perhaps none at all). How many working class (or even upper class) people do you know that have the slightest amount of power to sway policy? Me neither.
The rest is a question of whether believe it works, independent of whether they think it's a good or bad idea, and this is also irrelevant, mainly because working class are far more likely to be uneducated and may not have a grasp of mathematics and economics. The economics seem to be clear that austerity doesn't work. That means that the more important question is why has pro-austerity propaganda been so effective? We're seeing polls that show that the GOP is certain to gain seats in the coming elections, all while advocating policies that are likely to hurt far more of their voters than will help. What is it about their message that resonates? I really don't know.