Sending this many home will have a significant economic effect. President Obama is accusing the Republicans of wrecking the economy, and is holding crisis talks to reassure Wall St leaders.
The investment bank Goldman Sachs estimates that a three-week shutdown could shave as much as 0.9 per cent from US GDP in this quarter alone.
The government comprises 30 per cent to 40 per cent of New Zealand's economy and there would be a problem for any services or activities not already funded by an appropriation.
The Constitution Act says the government can spend money only with statutory authority. To do this, governments have to pass imprest and supply bills, but they can do so only if they have a majority in Parliament and the House has to meet to pass the bill. If there was no majority, the Opposition would instantly call for a vote of no confidence in the Government, which it would win.
The Public Finance Act does allow the Minister of Finance to incur expenses or capital expenditure without a parliamentary appropriation, but only in a state of emergency or civil defence emergency, or if a situation occurs that affects the nation's public health and safety.
Cost overruns on expenditure already appropriated is limited to no more than $10,000 or 2 per cent of the amount agreed to, and even that requires subsequent confirmation by Parliament.
The list of what could be affected in New Zealand could be long - healthcare, education, social security payments such as unemployment and domestic purposes benefits and superannuation payments, the courts, the police, the armed forces and public transport.
But unlike the US, New Zealand's leader - the Prime Minister - is part of the House of Representatives, and we do not have a warring House and Senate as the Americans do.
Importantly, in New Zealand parties that make up the Government promise to use their votes to guarantee supply. This means it is very unlikely that a Government would not be able to pass a budget.
If it could not, there would be a new election as it would have lost the support of a majority in Parliament, and the people would get a chance to elect different parties.
There have been fall-outs in New Zealand. During the first MMP government, the relationship between the National Party and New Zealand First broke down, and Prime Minister Jenny Shipley sacked Winston Peters as her Deputy Prime Minister. It was only by convincing rogue NZ First MPs to support National on confidence and supply that an early election was averted.
In the US, it's the first shutdown since 1995-1996, when Bill Clinton and the House of Representatives (and its speaker, Newt Gingrich) also failed to agree on a budget to fund federal services. That row lasted 28 days.
The US Government has partially shut down on 17 occasions. Democrats and Republicans are again staring each other down and unless a new deal can be struck, the Government won't be able to keep paying its bills.
If the NZ Government was ever in a similar situation, Kiwis would be reminded about the relevance of the government to everyday life.