Bernie Sanders is on the rise. Less than a week before the first contest of the Democratic primary, polls give the Vermont senator, on average, a 3-point lead in Iowa and an 8-point lead in New Hampshire. Nationally, he has climbed to within 5 percentage points of former Vice President Joe Biden. If Sanders wins the first two states, he has a strong chance of winning the nomination.

That sounds like good news for progressives. But it isn’t. Sanders has major liabilities that haven’t been exploited in the primaries. If he’s the nominee, those liabilities could hand the election to President Donald Trump. David Frum made this case on Monday in the Atlantic, and Jonathan Chait, writing for New York magazine, has backed it up with evidence from recent elections. But polls suggest that Trump has already identified a theme that would destroy Sanders: his socialism.

Trump is running on the economy, but he knows many voters don’t like him. He needs to give those voters something to fear about the other party. That’s where socialism comes in. Trump uses that word at every rally, hoping to make Democrats look radical and scary. Sen. Elizabeth Warren agrees with many of Sanders’ ideas, but she doesn’t call them socialism. Sanders does. He plays right into Trump’s hands.

If you hang out with young progressives, you might be under the impression that socialism is popular. It is, but only on the left. In the latest Gallup poll, taken in September, liberals and Democrats viewed socialism favorably, but Americans as a whole rejected it, 57 percent to 39 percent. In the same poll, respondents viewed capitalism favorably, 60 percent to 35 percent. A Harvard/New York Times poll, taken in July and August, found similar results: Americans endorsed capitalism, 57 percent to 37 percent, while rejecting socialism, 59 percent to 34 percent. Polls taken in May by the Pew Research Center, in March for the libertarian Cato Institute, and in December for Fox News yielded similar results. In every survey, socialism scores well among progressives but gets trounced, among voters as a whole, in a showdown with capitalism.

An American politician who believes deeply in socialism, as Sanders does, has every right to run as a socialist. But it’ll probably cost him. In November, a HarrisX survey asked, “Would you ever vote for a Socialist for elected office?” Liberals said they would. But 72 percent of registered voters, and even 64 percent of Democrats, said they wouldn’t. When voters were asked whether they would ever vote for a “Democratic Socialist”—Sanders’ preferred formulation—the percentage who said no dropped to 52. But that’s still a majority.

That number, 52 percent, is worse than it looks. It’s not just folks on the right. It includes 25 percent of Democrats and 29 percent of voters who “lean liberal.” Subtract those people from Democratic turnout, and you’re in trouble. Data for Progress, a left-leaning organization, found more encouraging numbers: In its survey, 62 percent of likely Democratic primary voters expressed a favorable opinion of “Democratic socialism.” But 17 percent, including 38 percent of Democratic primary voters who called themselves moderate or conservative, expressed an unfavorable opinion. That’s a segment of the electorate Democrats can ill afford to lose.

It’s possible that Sanders, through a combination of inspiration and campaign promises, could overcome the political drag of defending socialism. His net favorable rating in the electorate as a whole is pretty close to the ratings of his Democratic competitors. And some anti-socialist voters clearly like Sanders. A Rasmussen survey, taken in November for the conservative Heartland Institute, found that 20 percent of likely voters who expressed a very favorable view of Sanders also said they wouldn’t “vote for a presidential candidate who identifies himself or herself as a socialist.” Maybe these voters would set aside their aversion to socialism and elect Sanders.

On the biggest issue, health care, Sanders is proposing exactly what voters don’t like about socialism.

But that’s pretty optimistic. When people contradict themselves in a survey, the simplest explanation is that they’re not aware of the contradiction. What happens when people who say they like Sanders, but who also say they’d never vote for a socialist, find out he’s a socialist? How many of those voters can Democrats afford to lose?

You could argue that socialism is just a cosmetic term and that what really matters are Sanders’ policy ideas on specific issues. But on the biggest issue, health care, Sanders is proposing exactly what voters don’t like about socialism. Unlike Biden and other candidates who favor a “public option”—a government-run health insurance plan that would compete with private insurers, offering consumers an extra choice—the Sanders “Medicare for All” bill would explicitly make it “unlawful for a private health insurer to sell health insurance coverage” or for “an employer to provide benefits” that “duplicate the benefits” offered by the government. It would establish a state monopoly.

Every poll shows that the public option is a winner and Medicare for All is a loser. In a September NBC/Wall Street Journal survey, 67 percent of voters endorsed “allowing people under the age of 65 the option to buy their health coverage through the Medicare program.” Only 20 percent opposed that idea. But in the same survey, 56 percent of voters opposed—and only 41 percent favored—Medicare for All. That’s a 26-point loss of support for public health insurance, and a 36-point increase in opposition to it, when you shift from progressive capitalism to Sanders-style socialism.

Other polls show similar damage. In a December Fox News survey, 66 percent of voters endorsed “changing the health care system so that every American can buy into Medicare if they want to.” But only 41 percent supported “getting rid of private health insurance and moving to a government-run health care system for everyone.” In a December NPR/Marist poll, 56 percent of voters favored “a government-administered health plan … that would compete with private health insurance plans.” But only 40 percent favored “a national health insurance program for all Americans that replaces private health insurance.”

Sanders would let companies sell supplemental insurance that doesn’t compete with his government-run plan. But that doesn’t solve the political problem. In September, a HarrisX poll found that when voters were offered a choice among five health insurance systems, 10 percent chose the hardcore socialist position, that “Medicare/Medicaid should be expanded to cover all citizens regardless of age or income, and private health plans should be abolished.” Another 27 percent chose the Sanders position, that “people should be able to purchase private supplemental plans.” On the other hand, 19 percent said “the current healthcare system should be kept as is.” And 18 percent said “the government should remove itself from paying for all health care.”

That’s a 37 percent bloc on the left and a 37 percent bloc on the right. The remaining bloc of voters, 25 percent, chose the middle option: “Any citizen should be able to sign up for Medicare/Medicaid regardless of age or income, while those with private plans could keep their existing insurance.” Give those voters in the middle what they want, and you’re talking to a 62 percent majority. Abolish private coverage of basic health care, and you risk alienating a 62 percent majority.

Socialism and banning private health insurance are just the beginning of the case against Sanders. He’s promising massive benefits, with no idea how much they’ll cost, in a country where voters broadly oppose tax increases. He says all felons should be allowed to vote “even if they’re in jail.” And he has a history of statements and activism that would help Trump frame him as a crazy radical: promoting revolutionary Marxism, praising communist countries, opposing private charities, demanding the abolition of the CIA, and blaming female hormonal cancers on sexual repression and other “psychosomatic” factors. Democratic candidates haven’t used these old quotes against Sanders. Trump certainly would.

If you think socialism is important enough to risk losing the election, vote for Sanders. But if all you want is a progressive government—one that offers a public health insurance option, makes college more affordable, and mobilizes the country against climate change—you’re a lot more likely to get it by nominating a pragmatist. It feels good to vote for the candidate you admire most. But if Sanders wins the nomination and Trump wins the election, you’ll have four more years to feel the burn.