George Hawley, a political scientist teaching at the U. of Houston, has a trove of research papers on extremely relevant topics. For example:
Issue Voting and Immigration: Do Restrictionist Policies Cost Congressional Republicans Votes?
Forthcoming in Social Science Quarterly
Objective: I test the hypothesis that Latino voters were less likely to support Republican incumbents with strong anti-immigration records in the 2006 Congressional elections in comparison to Republicans with less restrictive records. I also test whether non-Hispanic white voters were similarly sensitive to incumbent immigration records when determining vote choice.
Method: To examine these questions, I created hierarchical models in which incumbent immigration records, individual views on immigration, and an interaction between the two were used to predict vote choice in the 2006 midterm elections. Individual-level data were provided by the 2006 Cooperative Congressional Election Study and incumbent immigration records were provided by NumbersUSA.
Results: This analysis found little [or] no evidence suggesting that Latino voters are less likely to support Republican incumbents with anti-immigration records. There was evidence suggesting that vote choice among non-Hispanic white was influenced by incumbent records on immigration, but the effect varied according to the respondent’s own views on immigration.
Conclusion: This study found no evidence that incumbent Republicans could increase their share of the Latino vote by embracing less restrictive immigration policies. In fact, doing so may cost them votes among non-Hispanic whites.
In other words, the conventional wisdom about Hispanics and Republican politicians is wrong.