It is a rallying cry, a grassroots campaign, an ideological obsession – and it just succeeded in shuttering the U.S. government for the first time in nearly two decades.

Tuesday's shutdown marks the culmination of a three-year battle by conservative groups to dismantle President Barack Obama's signature health-care law.

It's a cause that has the fervour of a crusade, driven by Tea Party groups who consider the Affordable Care Act – better known by its nickname, Obamacare – an unacceptable intrusion by the government on the rights of individuals.

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On Tuesday, there was no sign of a possible breakthrough. Republicans floated a proposal to reopen parts of the government in piecemeal fashion. A White House spokesman dismissed the suggestion, saying it showed "an utter lack of seriousness."

With no end to the impasse, Mr. Obama underlined Republican efforts to obstruct the health-care law. "This shutdown is about rolling back our efforts to provide health insurance to folks who don't have it," he said. "This, more than anything, else seems to be what the Republican Party stands for these days."

Most recently, Tea Party groups mobilized this past summer behind a last-ditch effort to starve the program of its funding. That set the stage for Monday night's confrontation, where the Republican-led House of Representatives refused to authorize any government spending unless key parts of the health-care law were delayed or altered, an offer then rejected by the Democrat-led Senate.

The result of this week's clash was a strange contrast that left the main goal of conservatives unrealized: On Tuesday, as government services closed down across the country, the health-insurance marketplaces at the centre of the Affordable Care Act opened on schedule (the source of funding for the law is not impacted by a shutdown).

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The law uses an array of carrots and sticks to ensure that the roughly 15 per cent of Americans without any health insurance will receive coverage going forward.

The fixation with thwarting Obamacare – a complicated law that enjoys only lukewarm support – carries major risks for Republicans. If the implementation of the insurance marketplaces turns out to be a logistical nightmare, the party could capitalize on its opposition to the law in the upcoming midterm elections, as well as the 2016 presidential race.

"There's a bigger calculation that has to do with 2014 and 2016," said Carlos Gutierrez, a former Secretary of Commerce under President George W. Bush. "The execution is probably one of the most complex things that this country has ever done. There are bound to be horror stories and unintended consequences."

But if the rollout is relatively smooth and Americans end up liking the law, the party's opposition to Obamacare will not yield electoral dividends, particularly among independent voters.

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"The only thing at the moment that's less popular than Obamacare is the way that House Republicans are handling it," said Steve LaTourette, a former Republican member of Congress from Ohio. "If Republicans continue to beat [Obamacare] up, it actually has a chance of becoming popular. Americans love the underdog."

The Republican resistance to Obamacare ranges from moderate members of the party who believe the law can be improved to those affiliated with the Tea Party who want to see the law abolished. Such members of the House of Representatives come from ultra-conservative districts ("not just red districts, but crimson," in the words of one long-time observer) where there is no need to moderate their position in order to win votes.

That has produced both principled opposition and over-the-top rhetoric with little basis in fact. "Obamacare is the most dangerous piece of legislation ever passed in Congress," Representative John Fleming, a Republican from Louisiana, said last month, according to a report in the New York Times. "It is the most existential threat to our economy" that the country has seen since the Great Depression, he claimed.

Republicans have disliked Obamacare since its inception, when it was passed with only Democratic votes. "A lot of us felt it was rammed down our throats," remembered Mr. LaTourette. Then, in the 2010 midterm elections, the recently passed health-care law "became the lightning rod around which the Tea Party and others began to gather."

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Stan Collender, an expert on the federal budget and a partner at Qorvis Communications, recalled attending a meeting between Republican members of Congress and leaders of state-level Tea Party groups in 2011. Their very first demand, he said, was to block a spending bill unless funding was stripped from Obamacare.

For the next two years, there was plenty of symbolism – the House voted more than 40 times to repeal or obstruct Obamacare – but no concrete action. "The frustration of being told they were going to get something, and not getting anything but procedural fixes finally boiled over," said Mr. Collender. "A large part of [the opposition to the law] is that it's got Obama's name on it."

This past summer, Tea Party groups and affiliated conservative organizations began mobilizing anew to urge Republicans to scrap Obamacare. In August, one such group – Heritage Action for America – held a "Defund Obamacare" town hall tour in eight cities. In September, Tea Party Patriots, a grassroots conservative organization, distributed a "Defunding Obamacare Toolkit" that included suggested letters to Congress, Facebook posts and Tweets ("Obamacare is a train wreck. #dontfundit #nomoretrainwrecks").

While that campaign energized the far right of the party, it also raised unrealistic expectations for rolling back Obamacare. Tea Party-linked groups "were saying 'This is the final stand, this can be achieved,' when the possibility of it actually happening was one in a billion,'" said Benjamin Quayle, a former Republican member of Congress from Arizona.