La commedia, mercifully, è finita. The US government is once more open, the country hasn't defaulted on its debt, and Republicans on Capitol Hill are now bitterly debating the political fallout from an entirely unnecessary crisis for which they were entirely responsible. And this mellow and misty autumn weekend, they need not look far for an answer – no further, in fact, than across the Potomac river, to the shores of the Old Dominion.

That unofficial title is said to have been bestowed upon Virginia by King Charles II, grateful for the colony's unswerving loyalty to the royalist cause during and after the English Civil War. Not that the loyalty endured. Two Virginians, George Washington and Thomas Jefferson, who would serve as the first and third presidents, were leaders of the War of Independence, while the fourth president, James Madison, took the US into the War of 1812 against Britain. On 5 November, however, a more peaceful political contest unfolds, as the state chooses its next governor.

Gubernatorial elections in Virginia are not quite like those elsewhere. Only there and in New Jersey do they take place in the political off-year after a presidential election. A second oddity is that, according to rules dating back to the days of Washington and Jefferson, the winner may serve only a single term. And for the last 40 years a third, unofficial, rule has applied: the party that wins the White House always loses in Virginia 12 months later. So, one would think, no problem. Barack Obama was re-elected in 2012, so a Republican win in Virginia next month is a sure thing. Not this year though, and the recent follies in Washington are just one reason why.

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If any state exemplifies the deep electoral predicament of Republicans at a national level, it is Virginia, former linchpin of the old Confederacy. Its domestic political loyalties thereafter were unswerving: first to Democrats when they dominated the South and then, in the post-civil rights era, to the Republicans. Until Obama came along, no Democrat had carried Virginia in a presidential election since Lyndon Johnson's landslide of 1964.

But in 2008 everything changed. And to prove his triumph was no fluke, Obama repeated the feat last year. Once a Republican certainty, Virginia is now a swing state that leans Democratic. Like the country at large, it has become more urban and more demographically diverse. Its political centre of gravity has shifted from the southern – and historically Southern – section of the state to the burgeoning suburbs around Washington, barely a mile from the Capitol building itself.

Old-time Virginians, once mostly Democrat but now Republican in allegiance, may detest what is happening, and refer to the northern rim of the state as "Occupied Virginia". But the trend is inexorable. As Virginia grows less rural, more cosmopolitan and more liberal, so does the US as a whole. Long before a few dozen Tea Party-type Congressmen recklessly tried to hold the US political system to ransom, the skies had been darkening for Republicans, losers of the popular vote in five of the past six presidential elections.

Even so, in November 2009 Virginia's unofficial law of gubernatorial elections held. The Republican Bob McDonnell was victorious, one of the first sure signs that Obama's national honeymoon was over. And it might even have held this year, too – until the government shutdown and the dance with a humiliating financial default. McDonnell, of course, was constitutionally barred from running again. But through the spring and summer Ken Cuccinelli, winner of the Republican primary, was even with, or slightly ahead of, his Democratic opponent in the polls.

One thing that Cuccinelli had going for him, it should be said, was the nature of that opponent. Terry McAuliffe is arguably the most prodigious, and certainly the most energetic, fundraiser in Democratic party history, but his ties with Virginia are tenuous at best. His image is of political hustler, salesman and operator. And, as he rarely lets an audience forget, he happens to be a very good friend of Bill and Hillary.

Alas, McAuliffe's hustle, bustle and general eye for the main chance remind you of everything you don't like about the Clintons. But since the Tea Party wrought its havoc, an analogous but far graver problem confronts Cuccinelli's campaign: he now reminds voters of everything they don't like about Republicans.

Not that there has ever been doubt where Cuccinelli is coming from. An impassioned opponent of abortion (who even pushed a "personhood" bill in Virginia, guaranteeing constitutional rights for an embryo from the moment of conception), he is a vigorous critic of immigration and has declared that homosexuality causes "self-destruction".

Again, these positions have for years been no secret. Cuccinelli's undoing now is surely his popularity with the Tea Party. That popularity reached new heights with his efforts as Virginia's attorney general, the state's top legal officer, to block Obamacare, the president's healthcare reform – the very issue the movement's zealots used as a pretext to shut down the government. And nowhere has that shutdown been more keenly felt than in Virginia's Washington suburbs, where tens of thousands of federal workers live.

Once level with or narrowly ahead of McAuliffe, Cuccinelli now trails his opponent by up to 10 points, and senior Republicans privately admit he has little chance of victory. If the contest was always a less than uplifting choice between the lesser of two evils, Cuccinelli right now is seen clearly as the greater one.

And, as in Virginia, so it goes across America. Republicans are perceived as being in the pocket of an extremist faction; the approval rating of the Congressional party is at an all-time low. Among moderate Republicans, meanwhile, the Tea Party's popularity has plummeted, from 46 per cent in June to just 27 per cent, according to a Pew survey last week. Maybe it's just as well that only Virginia and New Jersey are electing governors in November. For the Republican Party, the drama is only beginning.