Sure, that's what it means now, but only to keep the working class divided against itself.
What was the middle class became the nouveau riche and are now our current "one percenters." The old aristocracy is largely gone, though it hangs on in some places.
The middle class were the business owners and bankers. The middle class had servants. Towards the end of the industrial revolution, and especially after WWII, there was a push to provide the working class with many "comforts" of the middle class. This is when there was a push to homeownership (but only the spectacle of ownership, as it is likely that the bank will own the house far longer than the person living in it ever will after paying down a mortgage), the personal automobile, vacations (though even this is now disappearing), etc.
Simply having these once-luxuries available to the working class does not make that section of the working class the class equivalent of the middle class, as they do not own the means of production. They do not own the factories and the banks, but are rather beholden to them.
Furthermore, the Reagan-era demonization of the poor and working class was more successful than I imagine was even intended, and that's the real problem we're now dealing with. Step one was getting the working class to self-identify as middle class. Step two was getting those same people to actively participate in their own selling-out through a campaign of demonizing "the poor" - slitting their own throats.
Someone making $150,000 a year (and most aren't - the median is less than half of that) isn't in the middle of the person making $15,000 and the person making $2,000,000. If you're working for your money, you're working class.