Rather than a protest that impedes and obstructs, one that performs a community service would be much more effective.
For example, instead of obstructing a highway, how about doing a clean up of litter along the highway, with some kind of signage drawing attention to cause of the protest?
Many people are tied up in knots over the issue of illegal immigration. They do what leadership does. Blame.
When NAFTA was proposed and implemented, that drew millions to the southern border, from all over Latin America. Mexico had its own trouble with illegal immigration crossing THEIR southern border because of time taken to cross Mexico to OUR border, draining Mexican resources too.
I lived, worked, and hobbied on that border when NAFTA was really ramping up and maquilladoras were going up like new housing developments. The El Paso/Juarez metro area grew to 5,000,000 + people quickly, becoming the largest population on the border and second in Texas, just behind Houston.
The maquilladoras could not hire and employ all. Supply exceeded demand. That began the large scale flow of illegal immigrants into the US, across that border, because they were already there, had nowhere else to go, and no future.
A huge population of Americans are unaware of this history. I am only because I was there and saw it. For most, that border is a far away place in somebody else's back yard, about which all manner of stories and rumors proliferate because most people don't know and will never really know. Furthermore for most people, belief trumps knowledge.
NAFTA drew and continues to draw millions from all over Latin America to the border for factory jobs. That began influx of illegal immigration by people who did not get maquilladora jobs. If you take time to understand the history of this, you know a truth that makes your argument really powerful.
Combined with some form of protest that does good, it just might do something good for a change.