The ones that migrate within the rules of the country may have this effect, but if they're following the rules they're also protected by minimum wage laws and therefore have very little actual impact on wages.The reason I say this is that it's my understanding that the political right are largely in favor of a free market. Immigrants increase the pool of labor from which free market capitalism is able to draw from. Increasing the labor competition reduces the cost of employees on businesses.
This issue isn't the legal immigrant, who applies for citizenship and becomes naturalized, and pays taxes, and doesn't send the majority of the money they earn back to Mexico or India or wherever.
The issue is illegal immigration, immigrants that come in under the radar, come in on visas and never leave, sneak in to give birth to anchor babies, etc. They're often working off the books, for cash, which they often send back to their home countries.
And they're costing us billions.
I agree, every man has a right to work for a living.
Within the rules and laws of the society in which he seeks to work.
If he is not following those rules and laws, and his presence is creating expense and hardship for the people in the country that are following the rules, then no. He does not have that right.