There may be a relief rally in the US currency in the next two days, assuming all the legislation was passed, but the markets would continue to worry, Tennent-Brown said.
"I think the fact it's an 11th hour deal probably means there's no major change to our expectation that the US dollar is going to stay weak.
"If earlier on in the piece if they'd come up with a really solid deal with a really clear strategy for the years ahead they could've clearly averted a ratings downgrade.
Tennent-Brown said the US had a long way to go before it was in a position to solve some of its problems.
"The flipside is our currency is going to stay strong. But if you are trying to export into the US or attract tourists from the US that currency is going to be a bit of a headwind," he said.
The US debt deal raises the $14.3 trillion debt ceiling through 2012, and will cut spending by an estimated $1 trillion, according to Bloomberg.
In addition it calls for enactment of a law to cut another $1.5 trillion from long-term debt by 2021.
That's likely to see nervous investors who fled their US dollar positions in anticipation of a default, return to the greenback, with the kiwi and other currencies such as the euro likely to fall as a consequence.
Irrespective of the deal, traders will be anxiously watching for announcements from the rating agencies to see if the US will lose its triple-A credit rating, having already been placed on outlook negative by Moody's Investor Service and Standard & Poor's.
The likelihood of a cut was increased on Friday last week after US growth numbers for the second quarter came in weaker than expected, with the world's biggest economy expanding 1.3 per cent in the three month period, short of the 1.8 per cent rise predicted.
The sting in the data came with revision to first quarter gross domestic product numbers, with growth revised down to a 0.4 per cent expansion from 1.9 per cent previously.
"The reality is that even with a deal, the recent U.S. GDP data will be turning peoples' attention to the state of the U.S. economy," said Khoon Goh, head of market economics and strategy at Bank of New Zealand.
"Irrespective of budget cuts, what is clear is that fiscal policy is going to be a huge drag on the U.S. economy at a time when it is losing momentum."
The Australian cross rate is likely to be in the spotlight this week, with the Reserve Bank of Australia set to make an announcement on its official interest rate tomorrow.
The market is broadly expecting the bank to keep rates on hold at 4.75 per cent, although comments around the announcement are expected to be more hawkish after last week's Consumer Price Index accelerated at an annualised rate of 3.6 per cent, surpassing expectations for a 3.4 per cent gain.
That was the biggest annual increase since 2008.
The Bank of England and the European Central Bank are also set to make official rates announcements this week.
The ECB is expected keep rates on hold at 1.5 per cent as eurozone inflation falls, business confidence numbers slip and the market is plagued by uncertainties over how effective the Greek bail-out plan will ultimately be.
Bank of England, facing the twin challenge of stalling economic growth and rising inflation, is also widely expected to keep rates on hold at 0.5 per cent.
Commodity prices will also be in the spotlight this week, with the ANZ Commodity Price Index falling 0.1 per cent in July after June's 1.2 per cent decline.
That comes ahead Fonterra's GlobalDairyTrade auction on Wednesday, with economists seeing prices easing further after they fell 5.1 per cent to US$3,796 a metric tonne at the previous sale two weeks ago.
Also on the domestic data radar this week will be the release of the Quarterly Employment Survey and Labour Cost Index, and the Household Labour Force Survey for the June quarter.
The data is widely seen as showing an improvement into the local economy, although it is unlikely to move the currency, traders said.
- BusinessDesk / Susie Nordqvist