You have to remember the puritanical roots of the country.
The upper/middle/lower class distinctions are not economic:
- upper = rich;
- middle = comfortable;
- lower = poor.
They're instead based on morality:
- upper = blessed;
- middle = virtuous strivers;
- lower = good-for-nothing work-shy losers.
The upper class have been divinely marked for better things. They are never helped. Everything they receive is ordained. The lower class are scum who it would be wrong to ever help, since it would only encourage their inherent unwillingness to work. The middle class, then, are the self-made people who work hard for what they get and obviously deserve a little more, which in self-image terms is basically everyone.
Politicians promising to help the middle class are, therefore, declaring that they will reward the worthy (and punish the unworthy), which is a popular sentiment.