Yes. Reagan granted amnesty. McCain advocated for it. Did that get the Republican Party any loyalty? Did McCain win? Heather Mac Donald pointed out in her National Review article that US born Hispanics in California use public services at twice the rate of non-Hispanics and they vote that way. Immigration policy is not as important to them as public services. So if you don't promise more government goodies I'm not sure you will get the Hispanic vote.
BTW, I don't know any major conservative who advocates for deportation. The most I hear is closing the border and changing incentives so individuals self-deport.