"So, what do we do when the response from all of our leaders is a resounding, "Screw you!"?"
Playing to the media with mass counterprotests wouldn't likely work out; either a blackout or major downplaying in numbers would occur. Or, the counterprotest would be infiltrated with agitators, and the inevitable provocations would be played over and over again, painting the entire thing as racist.
Recall elections in states that allow them would likely get the point across. Boycotting businesses that clearly employ illegal aliens would likely get the point across. Voting any politico in support of amnesty would only be effective if their replacement were opposed.
That should be "voting out."
Forcing the governors of our respective states to deny tax-payer funded benefits and providing for stiff fines and/or jail time for those who knowingly employ them would cause them to deport themselves. End of problem. Trouble is, the "governing class" doesn't give a rip.