I don't think they are going to vote GOP. I do think the people who give the largest donations to the GOP like the cheap labor and, even if they are not using it directly, they benefit from the downward pressure on wages that comes with the package.
I think employers pay what it takes to get competent employees. There was a time, not long ago, that a visit to a fast food restaurant was a chore. The employees were incompetent, unreliable, often rude, rebelious toward managemnet, and many couldn't make change. They seemed to resent having to work. Those were good, young, bona fide Americans. Many were still students.
The same was true of most retail establishments. Rude, or indifferent, incompetent employees was the norm.
Then the immigrants started coming in. Most were here legally but not all. These were from all countries. Look at any 7-11. Although many at first had language problems they soon improved and we got better at understanding them. The big difference between the immigrants and the regular Americans was they were competent, reliable, and they appreciated the opportunity.
That is what turned the tide toward immigrants. Then in the last few years the flood gates opened and we have the situation we have today.
If immigrants underbid each other for jobs who is to complain. However, many immigrants are paid more than minimum because they are dependable and they work hard, something Americans had stopped doing. Not all are working for less than Americans will accept, they are paid more because they are worth more.
It is too easy to blame Bush, the Republicans, and employers but the real culprits are the Democrats (the Clinton Administration openly encouraged and abetted the flood, the Democrats in Congress are blocking anything from getting done, etc.), the labor unions who are losing members and want new recruits, the media who are leftists, and the socialists of all stripes who like the increased dependence on government. They like the out of control situation just as it is.
As usual, the media deflects the blame to the conservatives while they do all they can to exacerbate the problem. Too bad that many conservatives have become the useful idiots.