If you aspire to win a Republican presidential primary, do not mess with old people. Don’t believe me? Ask New Jersey Gov. Chris Christie in a few months.

Christie, whose chances of winning the GOP nomination had already sunk to Ted Cruz levels, released a bold Social Security proposal on Tuesday. Specifically, he wants to cut benefits for those making more than $80,000 a year, end them for those making more than $200,000, and raise the retirement age from 67 to 69.

There’s a reason Social Security is called the third rail of American politics. But Christie may be banking on the idea that his cuts would affect very few people: The plan wouldn’t apply to current seniors, and only about 10 percent of Americans earn $80,000 or more a year; only 1 percent earn at least $200,000. And that’s for all adults. It’s even rarer for retirees to earn that much. According to data from the Current Population Survey, 5.1 percent of Americans ages 69 and older (Christie’s proposed retirement age) earned at least $80,000 in 2013, and 0.7 percent — about 200,000 people — earned at least $200,000. Even those numbers actually overstate the number of people who’d be affected, because they include Social Security earnings, which Christie would exclude from the calculation.

Polling shows, however, that Christie’s making a bad political bet with this plan. (The plan has almost no chance of becoming law, so this is mostly about politics). According to a January 2013 Reason-Rupe survey, Republicans are more likely than Democrats, independents and the general public to say that income should not be a determining factor in receiving Social Security benefits. Only 26 percent of Republicans believe that Social Security should go to only those below a certain income level. Seventy percent of Republicans are opposed to such a proposal.

Among all Americans, 56 percent are broadly against changes like the ones Christie is talking about, according to the Reason-Rupe poll. The numbers are mostly the same across income and age levels.

Christie’s plan to change the retirement age affects many more people. When it comes to retirement, time is money: The average retiree gets about $1,300 a month in Social Security, so a two-year delay in retirement translates into more than $30,000 in lost income. That may be why older Republicans are very much against it.

In a September 2013 Associated Press-National Opinion Research Center poll, 58 percent of Republicans over the age of 50 were opposed to raising the age of eligibility on Social Security. Just 33 percent of Republicans over the age of 50 support such a proposal. According to an April 2013 Fox News survey, Republicans overall are more split. Still, does Christie really want to try to push the idea of raising the retirement age in New Hampshire, where 56 percent of primary voters are over the age of 50? For a moderate Republican like Christie, New Hampshire is a crucial state. His plan doesn’t seem like smart politics.

Among the general electorate, the plan to raise the retirement age is likely dead on arrival. The Fox News poll found that a majority (53 percent) are against it. Among those over the age of 50, 60 percent are against it, according to the Associated Press poll. For a party that is increasingly relying on older voters, this doesn’t seem like a smart strategy.

Now, I get that Christie is behind in the polls, and he may be making a play for “serious” Republicans. Indeed, Republican thinkers have been pushing for entitlement reform for years in order to cut the deficit. Former President George W. Bush tried it with his plan to partially privatize Social Security. More recently, Paul Ryan has called for reforms. Ryan, though, seemed to know that Social Security was a third rail. His most recent plan didn’t touch it.

Christie’s plan may very well set him apart from his fellow Republicans. But it’s likely to set him apart from Republican voters as well.

Ben Casselman contributed reporting to this article.