Obama's next task is to split the GOP Last week the US equity markets gave their verdict on the election, ending the week more than 2 per cent down from the start. The market's pessimism was clear: the probability rose on Tuesday night that the US will go over the fiscal cliff. To put it another way, Barack Obama's win sharply reduced the Republican appetite to avert a fiscal crisis. Which seems about right. There are occasions in a nation's politics when the overhang of decisions can no longer be contained. In the case of America's governability, this is the key equation: there is no path back to a half-decently functioning Washington that does not involve either a dramatic change of heart by the Republicans, or, less unlikely, a deepening split within it. Steep as they are, the stakes go far higher than the impending fiscal cliff. Should the GOP remain united in opposition to Mr Obama (who has a broadly centrist approach to America's economic challenges), the US will become cripplingly ungovernable. Look at California over the past generation. Alternatively, should the Republican party lose its iron discipline, and no longer reflexively act as a blocking minority in the Senate and a blocking majority in the House, events could turn out much better. The difference between gridlock and a restored climate of pragmatism is stark. Were the GOP to continue to block everything Mr Obama proposes, America's relative decline will accelerate. Conversely, if enough were regularly to dissent from their party's suicide pact, all sorts of possibilities would open up. Think of immigration reform, a cleansing of America's byzantine tax system, upgrading of US infrastructure, and even action on global warming. There can be little doubt this is also Mr Obama's prognosis. There are two reasons why his only realistic chance of success is to aim for a GOP split. The first is the reaction of most Republicans to last Tuesday's defeat - a prospect that few, including Mitt Romney, had entertained. Many have observed that the Republican party is in denial. Republican strategists blame the loss on everything from media bias to Hurricane Sandy. But the quandary runs far deeper than denial. Among the conservative Tea Party groups, Tuesday's vote only confirmed that the US is heading rapidly in the wrong direction. In their account, Mr Obama's Democrats have bribed enough of the undeserving poor with taxpayers" money to fall into their camp. As it happens, most of them are non-white. Rush Limbaugh, the influential radio host, fretted last week that "we are outnumbered." Quoting Corinthians on her Facebook page, Sarah Palin crystallised the belief that the election was a call to arms, rather than a moment for reassessment. "We are persecuted, but not forsaken, struck down, but not destroyed," the 2008 vice-presidential nominee wrote. This is the nativist wing of the Republican Party. Having in Mitt Romney fielded yet another Rino (Republican in name only), the party was punished for straying from its principles. It is a view shared by other powerful strains in the party, including the anti-tax powerhouse led by Grover Norquist. Last Friday, Mr Norquist said that any Republicans thinking of wavering on their anti-tax pledge would "be punished even for impure thoughts." Mr Norquist cited two of the four Republicans in the bipartisan Senate "Gang of Eight," who are up for re-election in 2012, as "eminently primary-able" - vulnerable to conservative challenges. The second thing going for a Republican split is there are also many who grasp the gravity of their party's direction. Ronald Brownstein, the Washington journalist, captures the GOP's demographic reality with his 80:40 rule. If Democrats win 80 per cent of the non-white vote and 40 per cent of the white vote, they are undefeatable. That is roughly what happened last Tuesday. At the Republican convention in August a clock showed the national debt. It should have kept demographic time. In Texas, the bastion of today's Republican party, the majority of schoolchildren are Hispanics. Each election, more will reach voting age. Some Republicans understand the import of this, among them probably John Boehner, the speaker (and figures such as former Florida Governor Jeb Bush). Mr Obama's goal will be to make it easier for Mr Boehner to argue for pragmatism within his party. But the US will first have to go over the cliff. Mr Boehner faces his own speakership election in January. He will not wish to jeopardise his grip by compromising on taxes before then. After the expiry of all the Bush tax cuts on January 1, he will be better placed to persuade some Republicans to vote for what would be packaged as a tax cut for 98 per cent of Americans - leaving the cause of the rich to another day. Thus, the US probably will go over the cliff. Whether, or how quickly, it will yo-yo back is harder to forecast. As a Roman once said, the victor is not victor if the vanquished do not agree. Last week's outcome left Washington's division of spoils unaltered - Mr Boehner's Republicans were returned to the majority. Through brinkmanship and seduction, Mr Obama must try to persuade enough Republicans to accept reality and then act on it. Whatever does happen, the next few months will offer gripping theatre. By February or March, we will be far wiser on the future of US governability.