Mayoral candidate Vincent Orange. (Tracy A. Woodward/The Washington Post)

The days on the calendar flip by, and the candidates in the middle of the pack, desperate to be contenders in the District’s April 1 Democratic mayoral primary, verge on panic. Here come the sharp-tongued assaults on the mayor. The hopefuls roll out wild promises to turn streets where jobless men hang out on corners into bustling boulevards of commerce. And then there’s the candidate who puts his faith in 5,000 bright orange wristbands.

“The weather’s getting better,” says Vincent B. Orange, the effusively optimistic at-large D.C. Council member who has been polling in the single digits. “And now I have my 5,000 wristbands. We give them out so I’ll be in front of people’s minds, and then I’m part of the plausible group.”

Nobody in this race wants to be the spoiler. The eight Democrats want at least to be plausible. But the math says one or more of them will shape the outcome by losing, drawing just enough votes from one front-runner to push the victory to another top dog.

Few significant differences on issues divide the mayoral candidates. That leaves the Democratic octet hammering each other on matters of personality, ethics, leadership and . . . plausibility.

While Mayor Vincent C. Gray urges voters to “stay the course” and council member Muriel Bowser (Ward 4) tries to cement her status in recent polls as the leading challenger, the candidates in the middle — Orange, restaurateur Andy Shallal, and Council members Jack Evans (Ward 2) and Tommy Wells (Ward 6) — all say they have a path to victory. The scenarios they paint often involve another candidate blocking their way.

As he goes door to door in the Mayfair section of Northeast, handing out “Orange for Mayor” wristbands and describing how he lost 55 pounds to prepare for this campaign, Orange spells out the complex formula by which he can win: “I need 15 percent in Ward 6, 15 in Ward 2, then I got to run the table in 5, 7 and 8, and I need all of the rest of them to split Ward 3.”

Wells, meanwhile, views everyone else as a potential spoiler, but he singles out Evans, the other white council member in the contest, as someone who is running not so much to win as to block him.

Evans is having none of it. “I’m running because I have experience unlike any of the other candidates,” he says. “Vince Gray is hobbled by the federal investigation [into his 2010 campaign], so he can’t be effective. And Tommy — Tommy, my God, is desperate.”

But arrangements among candidates to get in or out of a race are not foreign to American, or even District, politics. In 2006 in Pennsylvania, Republican supporters of Sen. Rick Santorum made every donation a Green Party candidate received to get him on the ballot, where he’d potentially take votes from Santorum’s Democratic challenger.

“When you’re an incumbent, it helps to have more people on the ballot,” Santorum said then. He lost anyway.

Four years ago, Gray saw one of his opponents in the Democratic primary, Leo Alexander, as a potential spoiler who could hurt him. Gray persuaded Alexander to drop out, The Washington Post reported last year.

“Spoiler” can be a painful slur, as Ralph Nader, Ross Perot and Robert Sarvis learned. As independent candidates for president, Nader in 2000 and Perot in 1992 won more votes than the gap between the major parties’ nominees, allowing academics and partisans to argue for years over whether the also-rans had delivered the election to someone who might otherwise not have won.

In Virginia last year, Sarvis, a Libertarian, won almost 7 percent of the vote in a contest in which Gov. Terry McAuliffe (D) beat then-Attorney General Ken Cuccinelli II (R) by only 2.5 percent.

Sarvis loathes the spoiler label, but he readily concedes that many candidates persuade themselves that they have a chance to win when they really don’t, a psychological defense against admitting they’ve devoted exhausting effort to a hopeless cause.

“You suffer a lot of indignities,” Sarvis says. “You introduce yourself to people and you see in their face that they’re thinking ‘I don’t need to pay attention to this guy.’ A lot of people say you’re doing this for your own vanity. You just have to ignore that. I knew it was very unlikely I was going to win, and it’s really liberating because then you can talk about issues that no one else will.”

Sarvis, at least, was running to advance an ideology — libertarianism — so he had a purpose beyond winning. In the D.C. mayoral race, even candidates with less than 15 percent support in the polls — which is true of six of the eight contestants — are out campaigning every day, attending forums almost every evening. Each believes victory is possible — standard thinking for potential spoilers, according to studies of the species.

“Candidates have a healthy ability to delude themselves, at least during the campaign,” says Robert Boatright, a political scientist at Clark University in Worcester, Mass., who has studied the motives of those who challenge incumbents. “But after the election, they almost always say they knew they weren’t going to win.”

Every also-ran can point to the moments in history when a purported spoiler did the impossible, although that occurs mainly when the incumbent takes a spectacular spill. In 1994, for example, one of the nation’s most powerful congressmen, Dan Rostenkowski (D-Ill.), was indicted on 17 felony counts and lost his bid for a 19th term to a largely unknown Republican.

One unusual aspect of the mayoral contest is that several candidates — including Evans, Wells, Orange and Shallal — entered the race assuming Gray would not seek a second term. The challengers thought the mayor would conclude either that he was too old, at 71, to take on a four-year commitment, or that he did not want to face voters with the U.S. attorney investigating corruption in his last campaign.

But no candidates dropped out after Gray announced in December that he would run.

“I thought the mayor wouldn’t be in it,” Wells says. “But now that he is, I’m even more committed because he has not explained anything about the corruption.”

Three weeks before the primary, candidates are abuzz over Gray’s status. The Post reported last week that Jeffrey E. Thompson, the prominent D.C. businessman who is at the center of the federal investigation into the illegal “shadow” campaign for Gray in 2010, is nearing a plea agreement with prosecutors. Gray has insisted he did nothing wrong and has refused to discuss in detail the actions that have so far led seven people affiliated with Thompson or Gray’s campaign to plead guilty in federal court.

Orange is one of several candidates who still believe — or hope — that Gray will withdraw before the vote. “I just don’t think he’s going to be there in the end,” Orange says. “The other shoe is about to drop. And if there’s a fumble in the next two weeks, I’m going to grab that fumble and run it in.”

Shallal argues that the mayor sought to have a wide field of opponents in an effort to slip into a second term even if, as a Post poll found, only 32 percent of D.C. residents see him as honest and trustworthy. “He wanted as many people in the field as possible to increase his odds,” Shallal says. “When I was deciding, I couldn’t get him to respond to me about whether he’d run.”

Shallal rejects the spoiler label, arguing that as an outsider who has never held office, he is not taking votes from other candidates but is expanding the electorate to include people who would stay home rather than vote for Gray or a council member.

Even as potential spoilers spurn the label, their status is both freeing and frustrating.

They try harder. At forum after forum, it’s mainly the ­second-tier candidates who work the room, scrapping for every vote, while the mayor rarely shows up and his most popular challengers, particularly Bowser and Evans, arrive a half-hour or even an hour late.

The underdogs speak their minds. They tend to be more blunt and therefore more likely to win the hearts, if not the votes, of people who attend forums.

Orange elicits cheers at a Ward 7 Democratic forum with a blast at Wells for advocating decriminalization of marijuana. “Tommy Wells is going to put drugs in our community!” Orange says, arguing that decriminalization would hurt young black men by luring them into the belief that it’s all right to smoke, even as employers still use drug tests to screen out marijuana users.

The trailing candidates try to cope with being ignored. At the National Democratic Women’s Club, candidate Carlos Allen, who barely registers in polls, starts to bash Gray’s school reform policies, but he can hardly be heard over the animated side conversation Gray and Evans are having on the dais.

“Who’s talking?” Allen says, sharply.

When the two ignore him and continue their chat, Allen raises his voice: “Excuse me!” Still chuckling, Gray and Evans pipe down.

Many voters dismiss candidates who do poorly in the polls as people “who are just looking for attention,” Boatright says. But there are other reasons such people run hard: They might be auditioning for a shot at another office sometime, or pressing a pet idea.

Or they might really want to be spoilers. “Tea party candidates, for example, often relish the idea that they’ve cost the incumbent the election,” Boatright notes. “There’s a long history in American politics of running to take votes away from somebody or to force them to shift on an issue.”

There’s no such talk on Foote Street NE as Orange chats up even residents who have Bowser signs on their front lawns.

He recites 16 lines of motivational poetry he learned as an Alpha Phi Alpha fraternity man: “If you think you’re beaten, you are. . . . The man who wins is the man who thinks he can.”

Orange beams. “This is life, and I’m enjoying it,” he says.

And if it doesn’t work out — well, he’s considered that, too.

“Look at Abraham Lincoln: The guy lost more than he won.”