It is a supply and demand thing. If the demand for labor remains constant but you increase the supply by adding lots of illegals then the price (wage) falls. The people who are hurt worst by illegal immigration are our citizens who are at the bottom of the economic ladder and have to compete with them for jobs. These are usually blacks, Hispanic-Americans and recent legal immigrants of all colors, races and creeds.
Dry wall hangers in Los Angelos used to make $18 per hour. Now illegals do this work for $8 hour. If a citizen wants to work at drywall hanging the excess labor of illegals is costing him $10 hour over what he used to earn and would earn again if the illegals were deported. The cost of housing has not fallen so this savings is not being passed onto consumers. It is being pocketed by the businesses that hire the illegals.
And that's the problem, you assume demand stays constant. More labor allows the economy to grow thus creating more demand for labor.