Do illegal immigrants have the right to make any sort of demands on legal citizens of the United States?

Demands? Sure. Protest all you want. It is a free country. One that I am honored to be a citizen of, and serve to the best of my ability. My mother is an immigrant.
Citizenship should be the goal for all of these people. And as fortune would have it, the path to get there is well-paved with over 200 years of experience. But they will have to want it. To push the paperwork through. To learn English and American History and Civics. If they want it, the American Dream can be theirs.
But that isn't what they want. They want the gifts and benefits of this great nation without doing the work to earn that right.
My grandfather, an Oberstleutnant in the Wehrmacht in WWII, turned carpenter/electrician in rural Minnesota, observed once to me that "people don't take care of what they get for free". Truer words were never spoken.
I would invite our friends from all over the world to come to America. It is still a land of opportunity for those who roll up their sleeves and get after it. But do it the right way.