PORTLAND — Republican Gov. Paul LePage claims to hate all politicians, but Eliot Cutler seems to be an exception. During the first gubernatorial debate last week, the incumbent governor of Maine treated his opponent like a frat brother — patting him on the back, punching him playfully, and high-fiving him.

The embattled governor, suffering from self-inflicted wounds and sagging approval ratings, has a good reason to show his rival a little love: if LePage holds on to his job, Cutler may well be the reason why.

With less than three weeks left, this year’s gubernatorial race in Maine is still an unpredictable — and unconventional — contest. LePage is hoping his core voter support is enough to win him a second term, making him perhaps the first governor in U.S. history to win two terms with less than 40 percent of the vote each time.

For Maine Democrats, the scenario is all too familiar. Four years ago, in another crowded gubernatorial race, Cutler pulled support from their party’s candidate. The independent came just 9,000 votes short of the governor’s mansion. The Democratic candidate came in third.

This time, Cutler’s support appears much softer. Polls show Democratic Rep. Mike Michaud and LePage locked in a tight race, with Cutler a more distant third. In September, a Portland Press Herald poll gave Michaud 41 percent of the vote, LePage 39 and Cutler 14.

Any incumbent with that level of September support is usually a sure loser. But the governor’s opponents are, in some ways, his greatest asset: just as in 2010, Cutler and the Democrat in the race are likely to split the considerable anti-LePage vote, which could well give the unpopular incumbent a solid shot at victory — one that would likely come with far less than a majority.

If Cutler weren’t in the race, the fall terrain would be far friendlier for Michaud: when participants in the Portland Press Herald poll were asked which candidate they would back in a contest between the two major party candidates alone, Michaud held a 50 to 44 percent edge over LePage. Seventy-one percent of the voters who backed Cutler in 2010 have a favorable view of Michaud, while 77 percent are unfavorable toward LePage.

The first debate of the campaign at Portland’s Holiday Inn By The Bay was, as in so many races this year, itself a question mark. When Cutler first proposed 16 face-offs in January, Michaud refused to participate, with his campaign describing the idea as a “stunt” and a “distraction.” LePage said he wouldn’t debate Michaud because of a Social Security attack ad. And Cutler called both men “cowards.” Eventually, the candidates compromised on five face-offs.

During the first clashes in Portland and Waterville last week, LePage kept his message focused on the GOP base. He is looking to ensure voters like Brian Brule, the co-owner of a local trucking firm, turn out in November. “I think Mike Michaud didn’t have anything strategic to say. Cutler doesn’t have the experience, and I think Paul LePage needs another four years. I voted for him before, and I’ll vote for him again,” Brule said after watching the Waterville debate.

Cutler may be losing the race for public support, but he’s winning the money chase. Reports suggest Cutler has had the biggest cash haul of any of the three candidates, bringing in $2.7 million through mid-September — at least $1 million of that from his own pocket. Michaud brought in $2.4 million and LePage $1.6 million.

LePage has received help this year from former Florida Gov. Jeb Bush and Gov. Chris Christie of New Jersey, the chairman of the Republican Governors Association, who has visited Maine four times to campaign with the incumbent. Cutler has the backing of Sen. Angus King, Maine’s independent former governor.

But Democratic heavy hitters are doing their best to make sure their party’s base stays on board this time: Michaud has enjoyed endorsements and help on the stump from former President Bill Clinton and first lady Michelle Obama, with President Barack Obama expected to campaign for him later this month.

Michaud is making an offbeat pitch in this restive year, selling himself as a consummate politician. He often refers to his many years of serving the state, both in the state legislature and Congress, in contrast with Cutler’s lack of political experience. If he were elected, Michaud also would be the nation’s first openly gay governor, though it’s a distinction he doesn’t play up on the trail. “Ultimately. . .this will be a non-issue,” he said.

During a forum at the University of Southern Maine on the governor’s race, a Cutler supporter said she had no qualms about supporting a candidate who did not appear to have a real chance of winning.

“It’s not a democracy if people can’t run,” said Wendy Payne, a Cashmere goat farmer. Payne, who called herself a Democrat, said LePage is “not real smart” — but preferred him to Michaud, who she said was “a nice man” but “not very visionary.”

“He’s not going to move the state forward like we need to right now,” she said.

Despite polling a distant third, Cutler says he remains confident — and unmoved by critics who’ve labeled him a spoiler. He has experience and name recognition earned during the last race under his belt as well as a motivated ground operation. “It’s deja vu all over again,” he said after the first debate, describing “buyer’s remorse” from Maine voters who “wished they hadn’t voted for LePage.”

Cutler dismissed Democratic criticism that his candidacy had no chance of success — and could hand LePage another term. “I’m spoiling this choice?” Cutler said in disbelief. “How can anyone spoil this choice? I’m not a spoiler, I am a choice.”