There are concerns whether Mr Obama and a Republican-dominated Congress will be able to negotiate a way to avoid the so-called fiscal cliff.
The cliff will see nearly $600bn (£375bn) of tax increases and spending cuts hit the US economy in January.
Japan’s Nikkei 225 index ended the day flat, South Korea’s Kospi rose 0.5% and Australia’s ASX 200 gained 0.8%.
The fear is that the tax increases and spending cuts that could be enacted if there is no agreement over deficit reduction may derail a fragile US economic recovery, and in a worst case scenario even push the economy into a recession.
“We head into the fiscal cliff, trying to find compromise where it wasn’t possible before,” said Rob Ryan, director of markets strategy, Asia-Pacific for Royal Bank of Scotland in Singapore.
The spending cuts and increased taxes are not the only concern among investors.
The US economy has been battling various other issues, not least the high levels of unemployment in the country, which have dented consumer sentiment and impacted growth.
Despite encouraging jobless numbers last week, unemployment continues to hover close to 8%.
There are concerns amongst some analysts that the jobs market may not improve anytime soon and that the recovery in the US will remain weak.
That does does not bode well for Asian economies as they rely heavily on US demand for exports and overall growth.
Investors have also been wary of the developments in the eurozone, where the Greek Parliament is set to vote on further budget cuts on Wednesday.
The parliament will vote on 13.5bn euros ($17.3bn; £10.5bn) of spending cuts, which include tax increases and cuts to pensions.
These cuts are key to determining whether Greece can get the next 31.5bn euro tranche of its European and International Monetary Fund rescue package.
Greece has warned that without this money, which will be used largely to recapitalise the country’s banks, it will be bankrupt by the middle of the month.
However, there have been protests in Greece against the proposed cuts.
Analysts said that there were fears that it may take some time before Greece is given the money.
“With Greece there are always a number of stages with any vote. It is a prolonged process to reach any conclusion,” said Justin Harper of IG Markets.
These concerns saw investors ditch riskier assets in favour of relatively safer ones.
Spot gold rose 0.5% to a one-week high of $1,724.21 per ounce in Asian trade, reversing a 0.6% drop earlier in the day.
Meanwhile, the Japanese currency, a traditional safe-haven asset, rose to as high as 79.81 yen against the US dollar from its four-month low of 80.68 yen.