"The market is getting used to these political shenanigans, games and brinksmanship," said Bank of New Zealand currency strategist Mike Jones.
"For the most part, the markets are snoozing it off and waiting for the dust to settle," he said.
The real issue facing markets would be failure to raise the debt limit by October 17, when stop-gap measures are expected to be exhausted and the limit becomes binding, which could lead to the US failing to pay its debts.
"It could well shake the markets if it is not handled properly," Jones said.
Of more immediate concern will be Friday's scheduled release of key US non-farm payroll data for September - the release of which is now in doubt because the Labour Department's Bureau of Labour Statistics is deemed to be non-essential.
Markets are placing greater-than-normal importance on the jobs report because a strong number could lead to the long-awaited wind-back of the US Federal Reserve's US$85 billion ($102 billion) a month quantitative easing activities.
Westpac senior currency strategist Imre Speizer said the market reaction so far had been muted.
"Historically, it's a big moment but most of it has been priced in, so there has been no reaction immediately," he said.
The New Zealand dollar firmed slightly against the greenback, trading at US83c from US82.9c just before the 5pm NZT deadline.
In the US today the chief executives of large banks including Goldman Sachs and JPMorgan are expected to meet President Barack Obama as Wall St urges Congress to end the budget stalemate in Washington.
The White House visit, confirmed by three people familiar with the schedule, was set up by the Financial Services Forum, a trade group representing the heads of the 19 largest banking and insurance firms.
While many Wall St firms have kept a low profile in Washington after the 2008 financial crisis, some big-bank chief executives have been speaking out on the danger posed by a prolonged political battle over fiscal issues.
In a talk last week at the Clinton Global Initiative, Goldman Sachs chief Lloyd Blankfein warned that the budget standoff was harming the US economy and markets.
The shutdown is estimated to cost the US at least US$300 million a day in lost economic output at the start, according to research company IHS.
That's a fraction of the country's US$15.7 trillion economy but the impact is likely to grow over time as skittish consumers and businesses stay on the sidelines.
- additional reporting Bloomberg