Sen. Graham greets his supporters during the Milford, N.H., Labor Day parade. (Charles Ommanney/The Washington Post)

Lindsey O. Graham has this election’s bleakest campaign promise: If elected, he will start a land war.

He would send American ­forces into the bloody chaos of Syria and keep them there until the Islamic State is no longer a threat to the United States. It is a grim, open-ended commitment: Even Graham isn’t sure when the troops could come home.

And hey! Here comes that big goofball now.

“Happy Labor Day! Good to see y’all! Sorry the government’s so screwed up,” a smiling, sweating Graham shouted, zigzagging from handshake to handshake, joke to joke, during this small New Hampshire town’s Labor Day parade.

“How you doin’? You watchin’ that post?” Graham said to a man who was leaning against a post. “Looks like a linebacker!” he yelled to a man with a small son. “Is that your house? Beautiful!” he yelled to a woman with a house.

“You want a photo?” he said, posing with a passerby. “Say ‘Flat tax!’ ”

Along the parade route, 10-year-old Joey Comeau watched this hustling, polo-shirted stranger approach and then walk over and offer him a fist bump. They bumped. Then Joey turned to his relatives, confused.

“Is he running for president?”

“Lindsey Graham,” said Rebecca Pollard, 25, Joey’s aunt, reading the candidate’s name from the signs his supporters were holding.

“Democrat, or Republican?” said Debbie Pollard, 55, his grandmother.

Graham supporters march in Milford. (Charles Ommanney/The Washington Post)

Graham, 60, is a Republican. He is a senator from South Carolina — and now a presidential candidate with poll numbers so low they aren’t even numbers anymore.

In several recent surveys, Graham didn’t even rate a numeral: Instead, he got an asterisk (pollster code for “less than 0.5 percent”) or a dash (code for something less than an asterisk, zero or nearly zero). Those numbers are so low that Graham will not be invited to a presidential “forum” next week, held just minutes away from his home in South Carolina. The bar was 1 percent, and Graham didn’t make it, according to the State newspaper in Columbia, S.C.

But even in the crowded back of the Republican pack, Graham is running a campaign so odd it stands out. He is a candidate with a spectacularly split personality.

On paper, Graham’s platform is essentially joyless. It offers GOP voters a menu of unpleasant options. War abroad. Fiscal cutbacks at home. Messy compromises with Democrats on Capitol Hill.

But in person, Graham the candidate often seems positively joyful, belying his gloomy message. He is the candidate of pain and suffering. But he is still a candidate, with a rare and energizing moment in the national spotlight.

“I think people have gotta see that I’m upbeat” in spite of the sacrifices he’s asking for, Graham said. “If I’m not optimistic, why should they be?”

Graham, who’s been in Congress since 1995, announced his bid for the presidency July 1. More than two months later, the logic of the thing still eludes some people.

At the Hilton Garden Inn in Manchester, N.H., the bartenders have started to worry a little about him, always visiting and sitting there alone. And back in South Carolina — where Graham won reelection just last year — even longtime allies wonder why he would choose to run, re-tapping old donors, for a goal so unlikely. One recent poll showed that just 4 percent of South Carolina Republicans wanted him to be president. Graham was tied for seventh in his own state.

“Folks really like him as our U.S. senator. . . . They like him in that role. That’s probably it,” said Glenn McCall, the state’s Repub­lican national committeeman. “He’s just doing such a great job where he is.”

When he first entered the presidential race, it appeared that Graham had a solid backup plan. If he couldn’t win, he could at least undercut one of his rivals: Sen. Rand Paul (R-Ky.), the libertarian-leaning candidate who is often skeptical of Graham’s calls for U.S. military intervention abroad.

Then things got weird.

Taking on Trump

Paul faded. And instead emerged another candidate whose platform was not so much antiwar as oddball war.

“Never thought I’d live long enough to see a candidate less qualified than Rand Paul” to command the nation’s military, Graham said. “Then came The Donald.”

Billionaire Donald Trump’s plan for the Islamic State — which many experts regard as unworkable — is to send American troops in to steal the oil out from under the bad guys.

Graham tried to undercut him. Trump responded not with an argument but with a prank: Onstage at an event, he gave out Graham’s cellphone number to the crowd.

So that didn’t work for Graham.

At times, it looks as if the sitting senator — and not the loudmouth billionaire — is the true oddity in this race.

In the past, plenty of rich men with attractive families have campaigned on the promise that they are special enough to give voters what they want (in Trump’s case, a border wall and better jobs) without requiring them to sacrifice for it.

But American politics hasn’t seen many characters like Graham: a single, childless 60-year-old promising to make voters suffer a little — just to keep what they already have.

“Sacrifice,” Graham said at the Iowa State Fair, summing up his campaign in a word. “Some of us have got to sacrifice to save this nation. . . . If I get to be your president, we’re gonna do the hard things, and we’re gonna do ’em together.”

In Syria, that sacrifice means a U.S. invasion — 10,000 troops, aided by Arab allies — sent in to defeat both President Bashar al-Assad’s government and the Islamic State. Graham says they will stay indefinitely, as long as it takes.

“We’ve been in Germany and Japan since World War II. We’re still in South Korea” 60 years after the Korean War, Graham said. That long, really? “I don’t know. I just know how it ends: We win. They lose.”

And he would send more troops back into Iraq, to help restabilize that fractured state. “Syria is Medicare,” Graham said. “It’s the hardest of all. Social Security is Iraq,” he said, which means it’s slightly easier.

Of course, Graham also wants to reform the actual Social Security and Medicare programs. His plan for both is to cut benefits for the wealthy in order to preserve full benefits for everyone else. He says his sister’s Social Security survivor benefits were invaluable after his parents died, and he tells voters they might be “one car wreck away” from needing that kind of help.

“I’m 60, I’m not married, I don’t have any kids,” Graham said at last month’s undercard Republican debate. “I would give up some Social Security to save a system that Americans are going to depend on now and in the future.”

In Graham’s plans, this is how you win.

It happens like this: He keeps visiting New Hampshire, which supported Sen. John McCain (R-Ariz.), his friend and fellow hawk, in two presidential primaries. Trump fades. Voters get real. Graham wins New Hampshire. It starts to build from there. Graham 2016.

Not yet.

“I see the numbers down in the polls. . . . It just really breaks my heart that I don’t see the numbers I want to see,” said Graham’s sister, Darline Graham Nordone. The two are exceptionally close. Their parents died when Graham was 22 and she was 13, and Graham helped raise her.

But, Nordone said, the poll numbers don’t seem to trouble her brother. In fact, she said, “I think he’s enjoying it a little bit.”

He is.

Behind but not bothered

“This is the first inning of a nine-inning game!” Graham shouted, as the Milford Labor Day parade kicked off under a blazing sun. The scene might have been discouraging for another candidate: Graham and his small entourage were positioned behind a somnolent band tootling jazz standards on a rolling trailer. And just behind him was a another, more popular candidate: Sen. Bernie Sanders (I-Vt.), who is shaking up the Democratic race, and his much larger following.

Graham’s cluster of supporters was quiet enough that, at one point, the crowd had to pump them up. “Make some noise, guys!” one woman said to them. Later, they started to chant: “Who’s the man?”

Then, before they could get to the answer (“Lind! Sey! Graham!”), a loudmouth in the crowd got his answer out first. “Don! Ald! Trump!” he said.

A parade viewer hits Graham with a water gun. (Charles Ommanney/The Washington Post)

Despite all that, Graham seemed to be enjoying himself immensely. At one point, he happened upon a group of young girls holding huge water guns. Graham, caught up in the fun of the day, held up his hands in a mock invitation to be soaked.

He didn’t think they’d actually do it.

The girls did. (They didn’t know who he was, the adults with them said later.) But Graham carried on, soggy and hot and far behind, and smiling and shaking hands.

“I got hit by a water terrorist!” he shouted at the crowd. Then a kid wanted him to pose for a selfie, and the candidate had a joke ready. “Say ‘I want my Social Security!’ ”