They recognize that America is a successful "entitlement" society. Americans have aided in the creation of that perception unfortunately, from the well-meaning "Nanny State" liberals to the cheap-labor-loving enterprise owners who do not care about the ultimate cost to the public at large. The problem with entitlement societies is that when those who are entitled to its benefits become vastly disproportionate to those who are paying for those benefits, the economic base degenerates under its weight and slowly spirals into decay. At some point the society can longer pay for all the benefits it showers upon its residents [of all classes] and it breaks down. Welcome to the Greece of today and California of tomorrow.
The people at these demonstrations do not want to become part of traditional America, its culture, or its values. They want to recreate America in their own image, and if you wonder what that is, just look over the fence. Now, I admit there are many many wonderful, loving, decent and intelligent people and many wonderful places in Mexico, but as a whole, their economic system, their culture, and their country has failed the common people there. Never has there been so many revolutions and so little progress as there has been in Mexico.
As for the protestors claim of entitlement based on their Hispanic, actually Native American [because in truth the Spaniards were merely the first of the white invaders] "birthright", I would remind them that their tribes didn't live here before the white man came. The present-day immigrants from Mexico are not of the same tribes as those who occupied the lands we now call California. The descendants of those native tribes number in a few thousands today. In their day -or were they in power today - they would have given a very rough reception to someone from south of the Rio Grande coming north to settle in their tribes' territories to claim the bounty of their lands. Ethnic solidarity based on "color" is a relatively modern invention. If you don't agree, study the history of the Aztecs and their ruthless subjugation and murder of their "brown" brothers, and get back to me.
(h/t Mark S.)