‘As Maine goes, so goes the nation.” It was a popular slogan about American politics until the 1936 presidential election. Alf Landon, the Republican nominee, carried Maine that year against Franklin D. Roosevelt – along with only one other state.

James Farley, an FDR political maestro, rewrote the slogan: “As Maine goes, so goes Vermont.”

But in 2016, Maine looks very much like the divided country we have become. It also has a longshot opportunity to play an important role in the presidential outcome. Only Maine and Nebraska divide their electoral votes by congressional district. While Hillary Clinton looks comfortably ahead in the state overall, several polls have shown her running behind in the state’s 2nd Congressional District.

If that district went to Trump, the state would give Clinton three electoral votes and Donald Trump one. And since there are a number of reasonably plausible scenarios that point to a 269-269 split in the Electoral College if Maine gave all four of its votes to Clinton, a single Maine elector going the other way could matter.

At the moment, this is largely the stuff of fantasy because it’s hard from the current polls to see Donald Trump getting anywhere near close enough to a majority for one electoral vote to make a difference.

Yet even if it does not prove electorally important, the split in Maine reflects social, economic and political divisions that are instructive for the nation as a whole. The state’s 1st District is more affluent, more liberal coastal Maine, including the hip and elegant city of Portland. The 2nd District is the Maine of struggling mill towns and rural areas. The 1st District looks a lot like the part of white America that is rallying to Clinton. The 2nd District looks a lot like Trump’s natural base.

On a visit here last week, I had coffee at Arabica, one of Portland’s delightful downtown cafes, with Dieter Bradbury, the deputy managing editor for news at the Portland Press Herald, and his colleague Kevin Miller, a reporter who has covered Maine politics, the environment and other beats for a decade.

“We have the perfect mix of the rural-urban split,” said Miller. “Especially in the 2nd District, we have a lot of mill towns that are struggling, and a lot of the mills are closing up. An “older white, male demographic,” he said, is sensitive to the decline in the lumber, paper, shoe and furniture industries. Cities such as Millinocket and East Millinocket have been hit especially hard by change.

Bradbury noted that not all of the difficulties can be ascribed to trade – consolidation within the various industries themselves has also played a role. But trade treaties, including NAFTA, are certainly a factor, and they open the door to Trump’s appeal.

Maine can also lay claim to Trumpian politics before Trump. The state’s controversial Republican governor, Paul LePage, has offended a large part of the state with an extraordinary range of comments to which the word “insensitive” does not do justice. In speaking of the war against drugs this summer, for example, he declared that “the enemy right now, the overwhelming majority of people coming in, are people of color or people of Hispanic origin.”

The comment led to calls for his resignation, but LePage hung on, bolstered by a passionate constituency of support that mirrors Trump’s. “Some people really love the governor, and a significant proportion of the population really dislikes him,” Bradbury said. “It’s a gap between the two that you can’t reconcile.” Bradbury added that LePage has said that Trump owes him a stipend or a bonus “for starting this whole thing about being outspoken.”

By the way, voters around the nation might take note of the fact that LePage won both election and re-election with a minority of the vote – only 37.6 percent when he was first elected in 2010 – because the moderate and progressive vote split, largely between the Democratic nominee and a third-party candidate.

As for that single electoral vote, Miller noted that the idea of the state splitting between its two congressional districts comes up every four years. This might, once again, be a case of misplaced speculation. But if there ever were a year when it could happen, he said, this is probably it. The social forces that are affecting (and dividing) the nation are as strong in Maine as they are anywhere in the country.