I think the allergy of the conservative base to illegal immigrant "amnesty", or anything close to it, is in interesting because I think there's something more to it than we've been hearing.
I don't believe it's mostly of the John Derbyshire variety -- he who felt the sting of going through all the legal hoops and and now feels the unfairness of illegals finding a path to citizenship. There aren't enough legal immigrants in the Republican party to explain that, and I think it's human nature that most people will not want to harshly punish someone getting away with something that they themselves would've done if they were in lawbreaker's situation. (Which is why Clinton got a pass from the Left -- most of the Left saw lying about sex as something they'd have done in his situation. Most of the Right didn't want to give him a pass because they couldn't imagine lying under oath no matter what it was about.)
Certainly the base feels like Charlie Brown when the football is removed the twentieth time just before kicking it. Neither party's elites are much interested in border enforcement and yet that's always used as a pledge of good faith when it comes to immigration bills. (This Administration comes by its negligence honestly; when we went into Iraq the borders remained open & thus invited Syrians and Iranians over to join the Baathists in a jihadist's wet dream.)
That's perhaps half the reason. The other half of the reason much of the base is repulsed by anything close to amnesty is fear that the illegals will eventually become voters. As Bill O'Reilly recently said (while reluctantly supporting the bill now making its way through the Senate), "The Republican Party will probably be wiped out. The new citizens are going to register three-to-one as Democrats, and we're going to have a one-party system because of this." The current office-holding Republicans can support it because they'll be out of office by the time it happens, and/or they see it as happening eventually with or without an immigration bill (i.e. demographics).
This may be the elephant in the room but is why the status quo will probably remain. That and the inability to predict how costly it will be to grant illegals legal status in terms of social services and such. Since there is no moral imperative to give immigrants citizen status, it likely not to happen out of political considerations. Btw, it's not just Bill O'Reilly who sees a big Democratic Party payday. Kate O'Beirne quotes the National Journal and Rep. Barney Frank:
Top Democratic leaders and activists see Hispanic migration as a long-term opportunity for the party. The arrival of additional immigrant workers is "bad for blue-collars," Rep. Barney Frank, D-Mass., chairman of the House Financial Services Committee, told National Journal late last year. But immigrants can help elect Democratic majorities, and "if [a Democratic Congress] were to significantly strengthen unions, then you would offset the negative effect on the income of workers," he said.