It's true that there's a nativist element in the Republican Party that talks about illegal immigrants as if they are sub-human. There are, as well, other Republicans more restrained in their rhetoric, but who give off the impression that they aren't huge fans of Hispanic immigrants. This definitely alienates Hispanic voters, but it is unclear to me that the passage of immigration reform would win over these people -- whether a reform bill passes or not, that element will still exist in the Republican coalition. So long as the questionable rhetoric continues, so will the mistrust...
If the bill passes, there won't be a huge surge of Hispanic voters over the Republicans: the party would at least retain a sizable portion of that vote (a lot more than the 1-2 percent of Black voters still voting Republican... yeah the last polling showed close to ZERO percent but I'm pretty sure there had to have been a few Blacks who went Romney... why I don't know, but I digress) and have a more diverse base of voters for the next Presidential cycle. But what would happen if the GOP House - with a sizable number of Far Right congresspersons who aren't huge fans of "illegals" and "freeloaders" - failed to take up the issue, to pass a similar bill that would get worked out in committee and sent to the President for a signature?
They'll still be in the same leaky boat in terms of Hispanic outreach, obviously, but the real damage will be to the Republicans' credibility as a functioning political party. It's not just the Hispanics they'll be losing, it will be the good-sized middle-of-the-road voters, the moderates or non-ideologue voters.
Even with all the obstructionist efforts the GOP has pulled since retaking the House in the 2010 midterms, there was at least this perception that the Republicans were, well, doing things. They'd at least tried to present some ideas in terms of budgeting and government oversight (albeit obsessed with tax cuts and deregulation as the CURE FOR EVERYTHING), they at least looked the part of a political party. Perception means a lot in politics: looking competent is more valuable than actually being competent.
But this would be the break with that perception, a huge one. There's been media buzz about the GOP fracturing ever since the earlier vote in the House for Hurricane Sandy relief that ended up passing without a majority of Republican votes. The House is now presented with a bipartisan Senate bill (as close to bipartisan as possible: it passed a Cloture vote, which is damn near miraculous this day and age), and a bill on immigration reform that the media (and thus the nation) perceives as a must-pass for the Republicans. If they can't even get this out of committee, the perception of party dysfunction would be overwhelming to everyone outside of the Tea-Party, anti-immigrant, anti-government crowd (and the Tea Party wingnut faction is not as big as the Fox Not-News commentators think it is).
There's not even a guarantee Speaker Boehner could pull off an attempted "poison pill" bill, something on immigration that would be so anathema to the Senate Democrats that the compromise committee that works on fixing disparate Senate-House bills would refuse to deal and thus give Boehner the excuse to blame the libruls. The wingnut faction of the House is so opposed to immigration they may refuse to vote on anything close to reform... and if there's enough of them, Boehner won't be able to get a floor vote on it, even with that poison pill. The blame will end up entirely on the GOP House. (if Boehner does get a bill passed with that poison pill, there's still no guarantee he'll be able to claim the Democrats killed it if the two houses can't agree).
The perception in politics will no longer be that "Congress is dysfunctional" because after all the Senate got something done. The perception will be "The Republican Party is dysfunctional." And while the Far Right won't be surprised or angry about it - after all, it's the kind of Party they want - whatever is left of the Center-Right and Moderate GOP voters (the RINOs that haven't fled yet) could well walk away.
The thing that always upsets me as an independent voter is that there's been enough middle-of-the-road, non-party-affiliated voters over the last 10 years who gave and still give the Republicans the benefit of the doubt. Having been burned by the Norquists and Limbaughs and Breitbarts that have taken over the party, I just couldn't grok how any moderate voters, any non-wingnut voters, were still voting for the ( R ) bracket. But one of the things about moderate voters isn't loyalty to a party, it's the desire to choose and vote for a candidate that creates and maintains an image of competency, of ability. They'll vote for a Republican if that Republican looks capable of walking and chewing bubble gum at the same time.
But a Republican that's part of a House of Representatives that couldn't even pass a symbolically important immigration reform bill? The perception of incompetence would be more destructive than the perception of that Republican being a hypocrite.
Despite the survival tactics that the Republicans use for midterm elections - the Congress-only, state Governor elections - that rely on low voter turnout and only the extremists voting, there's always the risk of playing it too close to the wire. While the average (read: moderate) voters won't turn out for midterms, they could turn out in enough numbers to voice their discontent against the party with the most at stake (read: the ones running Congress). During good years, the party in control tends to stay in control of Congress. During bad years, during sessions where the majority party is viewed as incompetent, failing, broken... you get the turnover. Look to 2006: the failure of leadership as the Iraq occupation turned sour was a major key to the Republicans losing to the Democrats in both houses. Look to 2010: the session-long struggle to pass health-care reform made the Democrats look out-of-touch and unfocused (even if they still passed it: perception, remember, counts for a lot), letting the Republicans retake the House.
The Republicans may have an advantage with gerrymandered districts that favor them despite the larger vote totals for Democrats, but a good number of those gerrymandered districts are stretched thin and more vulnerable than they seem. Get enough moderate Republicans and NPA voters disgruntled, get a Democratic candidate in one of those districts who can walk and chew gum, and you could well see a 51-48 victory for that Democrat.
The only things saving the Republicans at the moment are those gerrymandered districts and the possibility they can (and will) rewrite state voting laws to block all the voters they hate. But fail at this vote, fail to maintain even a semblance of competency... the Republicans can suffer even with the voters they hope would be on their side, the ones they'll let past the vote-blocking.
Try to remember this about the moderate/centrist voters: they vote for competency, not ideology. An incompetent Congress will lose those voters regardless of geography or gender or race. And there's more of us moderate voters than the wingnuts will admit. Count on it.