Sen. John McCainJohn Sidney McCainMcCain: Ivanka Trump, Jared Kushner had 'no goddamn business' attending father's funeral Meghan McCain: 'SNL' parodies made me feel like 'laughing stock of the country' Our military shouldn't be held hostage to 'water politics' MORE (R-Ariz.) said Tuesday that Republicans must address immigration, warning that if they do not it could cost them the White House next year.

“The reality is, is that we are losing support in the Hispanic community,” the Arizona Republican said. “We need to address the issue. We need to do it in a constructive fashion, or we do not win the 2016 election.”

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McCain is up for reelection next year, and will likely face a primary challenge. 

He visited the fence on Arizona’s border in 2010 and generally adopted tougher language on illegal immigration to win reelection that year.

But he said Tuesday that he’s worried GOP presidential candidates could hurt their party if they criticize immigrants too harshly.

He said that one of GOP 2012 presidential nominee Mitt Romney’s “biggest mistakes” was his comment about illegal immigrants self-deporting.

Romney said in 2012 that he backs “self-deportation, which is people decide they can do better by going home because they can't find work here because they don't have legal documentation to allow them to work here.”