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A duo of high-profile Republican primaries this Tuesday have provided even more ammunition for immigration reformers, who argue that the issue is no longer an albatross for GOP politicians.

That might be true on the surface, but the reality is much more complicated.

Last year, Sen. Lindsey Graham appeared to imperil himself politically when he decided to help write the Senate’s bipartisan immigration bill. But the South Carolina senator is poised to easily fend off a bevy of primary challengers on Tuesday. And in Virginia, House Majority Leader Eric Cantor is in position to coast to victory over an opponent who hammered him for not being conservative enough on immigration.

Those races — and others in California, Tennessee, and North Carolina — have fueled a narrative from immigration reform advocates that supporting reform is not an automatic death sentence for a Republican elected official.

In a Wall Street Journal piece titled, “Immigration’s Primary Effect Muted,” Graham pollster and reform booster Whit Ayres said, "So far, being against immigration reform is not the ticket to victory that a lot of the proponents of that point of view seemed to think that it was.”

Ayres is just partially correct. Immigration hawks who have challenged incumbents have lost a number of key primary races. That doesn’t mean immigration reformers are winning. Both Cantor and Graham have had to protect their right flank due to their openness toward more liberalized immigration laws.

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Cantor has done all he can to avoid being labeled “soft” on immigration. Primary challenger David Brat has accused him of leading an “amnesty drive” in the GOP-controlled House of Representatives. Brat, a college professor, was a virtual unknown when he entered the race, but he’s become a standard bearer for immigration hardliners. He was endorsed by conservative talk radio host Laura Ingraham, who has repeatedly heaped scorn on Cantor.

Facing criticism from the right, Cantor has eased off support for more liberal immigration policies.

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Last year, he was drafting legislation that would have provided a pathway to citizenship for young immigrants brought to the U.S. illegally as children. But Cantor, who controls the House’s floor schedule, has not allowed a full vote on any immigration-related measures since the Senate passed its bill a year ago, including one that would have granted young undocumented immigrants legal status if they serve in the military.

Cantor’s campaign recently circulated mailers that boast he “is stopping the Obama-Reid plan to give illegal aliens-amnesty.” The pamphlets were sent out even as Cantor was trying to reassure reform backers that he still supports the military bill.

Unlike Cantor, Graham has largely stood by his support for an overhaul, even though he’s been censured by local Republican groups and his opponents for not being conservative enough on key issues, including immigration.

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"What is in it for a Republican in South Carolina to be talking about this issue? Not much," he told The Wall Street Journal. He said the problems with the system were too big to ignore. "My goal is to fix it once and for all.”

But he hasn’t run as an outspoken champion of the issue, either. As PBS NewsHour notes, his closing TV ad plays up areas where he disagrees with President Obama, such as the Keystone XL oil pipeline, healthcare reform, and the Benghazi attack, and leaves out any mention of immigration.

And when a report last month claimed that the Obama administration released thousands of convicted criminals from immigration custody, Graham said it “sets everything back” in terms of passing a bill.

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Neither Graham nor Cantor are winning their races by playing up their willingness to work on immigration reform. They’re doing it by neutralizing their conservative challengers, who have bashed them on the issue.

So even though immigration hawks have struggled to claim a major prize this primary season, the results don’t necessarily mean that Republicans will rush to embrace an immigration push in this Congress or the next.

Jordan Fabian is Fusion's politics editor, writing about campaigns, Congress, immigration, and more. When he's not working, you can find him at the ice rink or at home with his wife, Melissa.