There's a significant percentage of native-born Americans who don't fit those criteria as well, aside from the part of wanting to become a citizen, because they got that right through birth.
I'm not saying that this changes the immigration issue, but if immigrants who, according to your estimation don't display the right attitude and motivation, who don't follow the law or set good examples for their children, and who don't look to America as a handout should be kicked out, then why shouldn't the native born Americans who possess the same characteristics be kicked out as well?
Many Americans don't even appreciate their citizenship, and are not even proud to live in this nation. They attain their citizenship through no hard work, simply by some sort of accident at birth that landed them here rather than in Mexico or Palestine or India or Wherever.
I'm not saying that we should treat this nation like some sort of Ivy League university, but there are plenty of people on the "Waiting List" and lots of people with "seats" who simply aren't pulling their weight.