People achieve this dream every day. I am not saying it is easy or a guarantee but if you look around, there are millions of people who have good homes, and have enough to raise their family. Many, if not most of them came from much humbler beginnings and I am sure their path to success was not without hurtles or setbacks.
Thing is, hard work may not be enough. You may also have to make temporary sacrifices in order to achieve that goal. For instance, instead of spending your hard earned cash on something you don't need, save it so you can afford to further your education. If you get a well paying job, you could get a reasonable sized house and afford to support a family. If you continue to advance in your career, you could afford to not only save for your kids education but maybe trade-up to a better home, car, and better vacation time with your family. Who knows, you might just be the next Bill Gates or your kids may be the next Walton family. After all, Sam Walton started by working in a grocery store and today, his family combined has twice as much money as Gates.
Granted, you will likely hit many bumps in the road. You could loose your job for reasons that are not your own, you might have financial hardships that make saving money impossible at the time. Nobody said it would be easy but if you sacrifice having some things you want now, you have a much better chance at getting where you want to be in the future.
Yes, you see many people achieving great wealth and success in today's society, but also note that most of them had always had a decent income. Take a company, for example. In today's society, entrepreneurs are taxed and regulated so much that it is almost impossible to survive without already having a decent income. Without a capitalist society, much of the success people see is based on their existing wealth.
The "American Dream" was the idea of working hard and having a big home and a family and enough money to support them, but in today's society with low wages mixed with the struggling economy do you think it is still a possible thing to reach or a likely thing for most Americans to reach.