The Hill has a blog item by Jennifer Martinez about how much money Silicon Valley (Bill Gates, Zuckerberg, et cetera) is pouring into the amnesty fight, and how badly they want the bill done:

One of the companies with a major stake in the outcome of the immigration push is Facebook, which has rolled out the red carpet for Republicans during their trips to the Valley.  

The company’s political action committee (PAC) has showered more than $100,000 in campaign cash on members of Congress this year, with contributions going to Cantor, Speaker John Boehner (R-Ohio), Senate Minority Leader Mitch McConnell (R-Ky.) and leading Democrats, according to the Center for Responsive Politics.

Facebook founder Mark Zuckerberg is also tapping his vast personal fortune to win passage of a bill that would help his company hire more foreign-born talent....

FWD.us ran ads supporting Sens. Marco Rubio (R-Fla.), Mark Begich (D-Alaska) and Lindsey Graham (R-S.C.) that touted their conservative bona fides. The ads for Begich and Graham noted their backing for the Keystone XL oil sands pipeline, infuriating green groups that had seen themselves as tech industry allies.
 
“Tech has sort of stuck its neck out on getting immigration done and getting it done in this Congress,” said a tech insider.

GOP's courtship of Silicon Valley put to the test in immigration fight, July 12, 2013

Two points:

1. The tech billionaires don't really need a full amnesty, all they need is a much smaller skilled immigration bill, that will bring in techies by the hundreds of thousands, but not import 30 to 70 million new immigrants from South of the Border, most of whom won't be high school graduates, let alone cheap programmers.
2. The Republican leadership, in  turn, should tell the Silicon Valley that it can't be done, for patriotic reasons. They can follow the example of Benjamin Netanyahu, who told the Israeli equivalent of the US Chamber of Commerce:

You will not like this, but we plan to legislate strict laws and enforce them with a firm hand against the illegal employment of infiltrators and foreign workers...  We are flooded with surge of refugees who threaten to wash away our achievements and damage our existence... He went on to say, "Anyone walking around Arad, Eilat, or even south Tel Aviv today, can see this wave, and the change it is creating, with their own eyes. They are causing socio-economic and cultural damage and threaten to take us back down to the level of the Third World. They take the jobs of the weakest Israelis."

[PM: Infiltrators pull us towards Third World Tani Goldstein Ynetnews.com, January 21, 2010]

It's that simple, once you've decided that patriotism is more important than campaign contributions.

Any other response amounts to openly accepting naked bribery.