The caricatured view of the Republican Party is that they are simply bought and paid for stooges who have no policy ideas beyond pursuing cheap labor, giving handouts to their corporate donors, and eager to get the country involved in pointless wars. Of course, confronting mass immigration would allow them to confront these perception problems and force the Democrats into a contest they can't win over the working class vote.
But you can always leave it to the Stupid Party to choose defeat.
Hill Republicans have all but surrendered the fight against President Barack Obama’s executive actions on immigration...But top Republicans say they’re not about to go there again: They tried that earlier this year with the Department of Homeland Security appropriations bill but were forced to capitulate on the eve of a department shutdown, having won no concessions on immigration. Better to let the issue play out in the courts, the GOP reasoning goes, especially since a judge has already halted the president’s November executive actions — at least for now...With the GOP in control of both chambers, party leaders are determined to avoid no-win showdowns with the Obama administration. Democrats still control 46 seats in the Senate — enough to keep Republicans from the 60 votes they need to advance legislation and to keep leaders focused on measures that can win some bipartisan support. Another scorched-earth immigration fight risks more congressional gridlock, just as Speaker John Boehner (R-Ohio) and Senate Majority Leader Mitch McConnell (R-Ky.) hope to secure deals on trade, cybersecurity and Iran.["Little GOP appetite for immigration fight on homeland bill, by Seung Min Kim, Politico, May 5, 2015].