But last Tuesday, when 800,000 US public employees were told to stay at home, there was no disguising their excitement.
"We've passed the witching hour of midnight, and the sky didn't fall," said Iowa congressman Steve King. "Now the pressure will build on both sides."
Steve Pearce, elected to the House of Representatives in the Tea Party wave of 2010, said he could not, in good conscience, cast a vote to keep the government open. "At times, you must act on principle and not ask what cost," he said.
President Barack Obama has accused congressional Republicans of demanding "a ransom just for doing their job". The Democratic leader of the Senate, Harry Reid, has called the hardliners "banana Republicans". Chances of a negotiated settlement appear remote.
Congressional scholar Tom Mann, of the Brookings Institution, said it is unprecedented for the party in opposition to refuse to fund the government on policy grounds.
"This is a matter of saying: 'Give me all your money or I'll shoot your children and if you don't, then you will be the murderer,'" Mann said. "The Republican establishment made a pact with an extreme populist, radical force. Now they're being controlled by that element, and they're terrified of rejecting them."
However, those who are holding out are by no means universally popular with their fellow Republicans.
Influential conservative commentator Charles Krauthammer dubbed them "the suicide caucus". California congressman Devin Nunes, one of the most vocal moderates in the House, went further. "[They are] lemmings with suicide vests," he said. "They have to be more than just a lemming. Because jumping to your death is not enough."
Congressman Mark Meadows sent an open letter to House Speaker John Boehner in August, urging him to "affirmatively de-fund the implementation and enforcement of ObamaCare". It was signed by 79 other members of the House.
Many of the leading refuseniks were members of the "birther" movement that questioned whether Obama was born in the US. "It's the most disturbing development in American politics in decades," said Mann. "One of our two major parties does not accept the legitimacy of the other party. Obama's not a real American, probably born in Kenya, probably a Muslim, certainly a socialist, as are all the Democrats. The evidence for that is ObamaCare, which was originally a Republican plan for health reform, passed and implemented under Governor Romney in Massachusetts."
Republicans have already won the budget battle. The resolution passed by the Democratic-controlled Senate to keep the government open did so at "sequestration levels" - accepting the brutal cuts to public services imposed during the last funding impasse as a given. The House rejected this, despite a Quinnipiac University poll showing that 72% of Americans oppose shutting down the government to block ObamaCare.
And so it is that 97% of Nasa's staff have been told not to show up for work, nine million people dependent on the women, infants and children nutrition programme will soon stop receiving food assistance, the Environmental Protection Agency is all but closed and another 1.3 million "essential" public employees are working with no guarantee they will be paid in the near future.
Polls consistently show an even split between people opposed to and in favour of the Affordable Care Act, but it is difficult to assess public opinion, not least because many of the Act's major provisions only came into effect on Tuesday.
The shutdown is simply the latest episode in a long campaign of Republican obstruction. The House has voted to repeal ObamaCare 43 times, and 26 states controlled by Republicans have rejected federal funding to expand Medicaid, the state health scheme for people on low incomes, even though the government will pay all the costs until 2016 and no less than 90% thereafter.
Many of the same states are refusing to enforce parts of the law which stipulate that insurers must accept people regardless of pre-existing medical conditions. In Missouri, local officials have been barred from doing anything to help implement the law. "Let me tell what we're doing," Georgia's state insurance commissioner Ralph Hudgens told his fellow Republicans. "Everything in our power to be an obstructionist."
FreedomWorks, the leading Tea Party organisation, is encouraging young people to "burn their Obama-Care cards" - though no such cards exist - in the hope that by persuading them to pay a fine rather than get insurance, the pool of insured people will be older, sicker and more expensive to cover, dooming the scheme.
In television adverts paid for by billionaire libertarians the Koch brothers, a creepy Uncle Sam pops up behind a man about to get a prostate exam and in front of a woman with her legs open on the gynaecologist's stretcher. The message? "Don't let government play doctor."
"All across this country Americans are suffering because of ObamaCare," began senator Ted Cruz, kicking off an epic 21-hour protest speech on the Senate floor. But on the first day of enrolment, the New York State Health Exchange logged 10 million page views and the federal healthcare portal frequently crashed due to high demand.
"I think the Republican party leadership are afraid," said Shane Larson, legislative director for the Communications Workers of America. "They don't want to give Obama anything that the public might like as time goes on. But I do believe that there is a core of Tea Partiers who have an extreme ideology that all government is bad."
Meanwhile, the Tea Party is digging in. "We're not going to be disrespected," Indiana congressman Marlin Stutzman told The Washington Examiner. "We have to get something out of this. And I don't know what that even is."