And so – absurdly, shamefully and almost incomprehensibly – it has come to this. The legislature of the richest, most powerful country on earth, that likes to present itself as a model of democracy and good sense, has failed in its basic task of providing funds to keep the federal government running.

Of course, not everything will shut. The US military will not be affected, and those, like air traffic controllers and prison guards who perform vital services, will remain on the job. In many parts of the country, the impact will be little felt, at least to begin with. But for 800,000 federal workers deemed less essential, days or weeks of unpaid lay-offs beckon. How on earth did it come to this?

President Obama was left to rail against the "ideological crusade" against Obamacare, vowing not to "give in to the reckless demands by some in the Republican Party to deny affordable health insurance to millions of hard-working Americans".

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In some respects, what is happening in Washington DC is not unusual. America has a presidential system, not a parliamentary one like Britain. Here, the annual federal budget the White House sends Congress is merely an opening gambit. On Capitol Hill, the process restarts from scratch. If control of Congress is divided, as now, no budget may be passed at all.

Indeed the last time a budget was enacted fully and on schedule, with separate appropriation bills for government departments, was in 1997. But recently the deadlock has worsened. An overall spending bill has not been approved for three years. Stopgap “continuing resolutions” (CR), which keep government open while the Republican-controlled House and the majority-Democrat Senate bicker, have been the norm. At midnight on Monday the latest CR ran out. Congress could not agree on a new one.

Further reading

Latest news: Obama vows not to give in to 'ideological crusade'

Q&A: All you need to know about the crisis in America

Matthew Norman: US shutdown isn’t serious, but reasons behind it are

Editorial: There could be so much worse to come

Nor is a shutdown without precedent. The last – and at 21 days the longest – occurred in 1995-96, during Bill Clinton’s first term. Indeed it was during that enforced idleness that the President began his fateful dalliance with Monica Lewinsky. But when it was over, no serious economic damage was done. This time, however, things look different.

Back then, the economy was strong. Today, recovery from the 2008 financial crisis is still fragile. At the very least, the closure and the accompanying lay-offs will reduce consumer confidence and spending. And in a deeper sense, the impasse reflects an ever more polarised and dysfunctional political system, where compromise is a dirty word.

Both sides are to blame. But the root of the problem, beyond argument, is a Republican party that is losing touch with reality. Even its control of the House of Representatives is a distortion. In the Congressional vote in 2012, Democratic candidates polled half a million more votes. But thanks to gerrymandering by Republican-run state legislatures, the GOP ensured itself a majority.

Gerrymandering, in turn, has led to safer seats, in which the danger to an incumbent is – increasingly – less the general election in which he faces a Democrat, than a possible challenge from a more conservative fellow Republican in the primary. That in turn has pushed the Congressional party further to the right, allowing the minority Tea Party faction to make the running. More centrist, pragmatic members fear to make deals with Democrats that will be held against them by the hardline activists who dominate primary voting.

The 1995-96 crisis ended when the Republican Senate leader Bob Dole went on the chamber floor and declared in so many words: “Enough.” Dole was about to launch a White House bid, and was anxious to project himself as a moderate and problem-solver. How different now.

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The current Republican leader, who might be expected to lead efforts to secure an agreement, is Mitch McConnell of Kentucky. But Mr McConnell is not running for president. Instead, he is most worried about a potential primary challenge from the right, as he seeks a sixth Senate term in 2014. A display of pragmatism might doom him.

Back then, too, the Republican House was led by Newt Gingrich, then at the height of his powers, who got on well with Bill Clinton, despite their ideological differences. John Boehner, today’s Speaker, is no Gingrich. Instinctively he is a deal-maker, but his priority is to avoid a confrontation with the Tea Party that could cost him his job.

Polarisation has also broken down old conventions on Capitol Hill. The Senate and House used to be completely separate, even rival, entities – but no longer. One extraordinary feature of this crisis has been the spectacle of Ted Cruz, the firebrand Republican first-term senator from Texas, organising House conservatives in their resistance.

Which leads to a third difference with 1995-96. That shutdown was a dispute about fiscal policy, the eternal debate over taxes and spending. This one is about policy, namely President Obama’s 2010 health reform, whose delay (and ultimately demise) Republicans seek as the price of a new CR.

The classic definition of insanity is to go on doing the same thing, and expect a different outcome. And so it is now. The Republican House has passed 40-odd resolutions to overturn Obamacare, and each time the Democratic Senate has said, no. Now it is trying again, and the outcome – utterly predictably – is the same.

What happens next is anyone’s guess. The public blame the Republicans for the shutdown; even the US Chamber of Commerce, normally a staunch ally, has expressed displeasure at the party’s tactics. For his part, President Obama vows not to give an inch. So, however, do the Republicans.

Something, sooner or later, will have to give. Perhaps public fury will shame Congress into a deal. But don’t bank on it. Even before this debacle, Congress’s approval rating was barely 10 per cent, making it marginally less popular than colonoscopies or communists. The institution, it would appear, is beyond shame. Just possibly, the crisis could provoke a rupture within Republican ranks. But again, don’t bank on it.

And this could be merely a warm-up. On 17 October, the US will hit its federal borrowing ceiling and unless Congress authorises an increase, could default on some debt, risking chaos in global markets. Absurd, shameful, incomprehensible? Indeed. But that’s the American way of government in this autumn of 2013.