Why is this so hard to figure out? The competitive nature of the game of cable news commentary sometimes obscures the obvious. Nobody wants to stare into the unblinking eye and repeat the same thing that everyone else has already said. So all kinds of other theories are being floated. But Eric Cantor was defeated because he become viewed as unreliable on the issue of white nationalism. And white nationalism is at the core of today's conservative movements.
The anti-immigration reform tendency is a pure expression of white nationalist ideology: the preference for a country in which white Europeans dominate, and others are kept to the margins. White nationalism explicitly drove our immigration policy for most the country's history. It was only during the 60's that explicit quotas based on present proportions of US population were dropped from legislation. But white nationalism is still deeply embedded in popular consciousness.
Picture "Real Americans" in your mind; if you are white, you know who shows up: white people. Yes, you know better, and will rapidly revise your picture to make your snapshot of "Real Americans" more accurate. But your first association of whiteness with the national identity shows the grip of white nationalism in popular consciousness. That is pretty understandable: whites have been steeped in white nationalist mythology all our lives. We had to unlearn that Columbus discovered America. It took a while to discover that comparing African Americans to "other" immigrant populations was a false comparison. We are still learning that it is the white residents of Arizona and New Mexico (even though they are our parents and grandparents) are the invaders. The patterns of housing segregation have perpetuated an unrealistic perception of who Americans are in most white people.
We would like to think that if we do not actively dislike and demean people who are not white, then we are not racist. Leaving aside for the moment the whole argument about power and privilege, I would remind all that you don't have to be a bigot to be a white nationalist.
The sense that the United States is supposed to a white nation is what is threatened by simple fact that immigrants from Latin America, Asia and Africa are outnumbering immigrants from Europe. The USA is getting to be less European with every passing year. On a national level, the country is already run by multi-racial voting coalition.
White nationalists are fighting back by trying to prevent comprehensive immigration reform. They're not stupid; they understood that Eric Cantor was going to play a key role in immigration reform this year. So he was defeated. Why we don't want to look that in the face is beyond me.