Soon-to-be-former House Majority Leader Eric Cantor encapsulates perfectly the Republican dilemma on immigration.

Immediately after Cantor conceded his Republican primary in Virginia to a candidate to his right on immigration, liberal activists stormed the ballroom housing what was supposed to have been Cantor's victory celebration.

"What do we want?" they chanted. "Immigration reform! When do we want it? Now!"

Cantor was thrown out of office by Republicans who were, among other things, anti-amnesty. He was then immediately protested by liberal supporters of comprehensive immigration reform.

Talk about a no-win situation.

For Republicans, immigration is the ultimate "heads I win, tails you lose" political issue. And that's not just because it's a contentious debate that pits a vocal part of the GOP base against a growing demographic group.

Many Republicans fervently hope that their problems with Latino voters will simply go away if the GOP crosses the aisle to help pass immigration legislation. At least, they reason, this would earn Republicans a hearing with a critical and growing voting bloc.

Unfortunately, the evidence for this proposition is very thin. In 1986, Washington enacted immigration reform legislation, including what was openly described as amnesty for illegal immigrants.

This bill passed a Republican-controlled Senate and was signed into law by President Ronald Reagan. Yet the Republican share of the Latino vote was actually smaller in the 1988 presidential election than it was in 1984, before amnesty passed.

In 1990, President George H.W. Bush signed a bill that increased legal immigration by 40 percent. It also created a smaller temporary amnesty program for the spouses and children of people who had benefited from the 1986 law.

Bush's share of the Latino vote fell even further, tumbling all the way down to 25 percent. This was after two major attempts at immigration liberalization and before California's Proposition 187 (which banned most public services for undocumented immigrants), Pete Wilson's re-election, and most other events frequently blamed for turning Latinos against the Republican Party.

Granted, that was a rare three-way presidential race held in the aftermath of a recession. It's doubtful Bush's immigration stance was a reason for his poor performance. But it plainly didn't help.

If genuinely bipartisan legislation signed into law by Republican presidents did not win over Latino voters, why would legislation receiving more Democratic than Republican votes in Congress that is signed into law by Barack Obama? (These earlier laws also didn't curtail illegal immigration, but that's another story.)

Also important: Latinos care less about immigration than comprehensive reformers assume. A 2013 Pew Research Center survey found that 57 percent of registered Latino voters considered education an "extremely important issue," 52 percent said the same of jobs and the economy, and 43 percent picked health care. Only 32 percent said immigration.

In 2010, immigration was ranked as the fifth most important issue for Latino registered voters and fourth for all Latinos. Registered Latinos ranked immigration below the federal budget deficit and barely above the environment and the war in Afghanistan.

That doesn't mean immigration is irrelevant, of course. Three-fourths of illegal immigrants in the United States are Latino and more than 90 percent of those deported recently are from Latin America. Pew found that 46 percent of all Latinos and 59 percent of Latino immigrants worry "a lot" or "some" that they, a family member, or a close friend might be deported. Clearly, immigration reform matters. But it isn't the only or even the biggest issue for Latino voters.

Often what happens is that the immigration debate is used as a proxy for whether Republicans care about Latinos. That's exactly how Democrats frame the issue each time Republicans vote down reform legislation. If Republicans don't partner with the left on immigration reform, they get crushed as being anti-Latino.

And if Republicans do support immigration reform? It hurts them politically at both an individual and party level.

If immigration reform makes immigrant voting blocs larger without making them more Republican, GOP reformers become like the store owner who loses money on every sale but hopes to make it up on volume.

And thanks to the opposition of many conservative primary voters to such legislation, Republicans like Cantor who try to show even limited support for immigration reform can easily find their stores under new ownership.

Don't assume this is just about Cantor. What happened in Virginia has as much to do with the intractability of the problem as with Cantor himself. And that's a lesson Republican lawmakers would be wise to take to heart.