President Obama needs to secure a deal with the US Congress to avoid the so-called “fiscal cliff”.
This refers to the $600bn (£375bn) of tax rises and spending cuts that are due to hit the US economy in January.
There was little reaction to President Obama’s victory result on the markets, with shares in Europe up slightly.
The main share indexes in the UK, Germany and France were up by between 0.3-0.5%.
Michael Hewson, a senior analyst from CMC Markets, said the markets had “adjusted to the fact that there would be continuity with respect to the economic policies of the last four years”.
“What it doesn’t change is the problems facing the US economy, and the roadblock that is the fiscal cliff.
“Once the euphoria of an Obama win has died down, this is likely to be the one thing that markets and investors focus their attention on,” he said.
The tax rises and spending cuts are currently due to come into force across a number of days in January.
They include everything from the end of a tax relief scheme for middle earners, to a reduction in how much doctors are paid by Medicare, the government-administered healthcare programme.
Some of the tax rises apply to the timetabled end of relief schemes started during the administration of George W Bush.
The fear is that if the fiscal cliff is not avoided, it may derail a fragile US economic recovery, and in a worst case scenario even push the economy back into recession.
However, President Obama, a Democrat, faces a difficult challenge in securing a deal with Congress because the opposition Republican party has maintained a majority in the House of Representatives, the lower house of Congress.
The Republicans want to see a general fall in federal spending to help reduce the US budget deficit, and the amount of money that the administration has to borrow to cover the shortfall.
The Democrats also want to reduce the deficit, but favour doing so more through higher taxes, primarily on higher earners.
The BBC’s economics editor, Stephanie Flanders, said that half of the timetabled tax rises and spending cuts may come into force, but others would be harder to reach agreement on “with both sides so angry”.
“The Republicans don’t want to see defence spending cuts, which will happen if they don’t reach a deal, but the Democrats are just as keen to ensure that the very richest see tax rises, something that the Republicans don’t want to see.
“So I don’t think we are going to see an early solution on that unless Republicans decide this was a real mandate for Obama’s policies, and I’m not sure they will given that it was still relatively close.”
Jeff Cleveland, senior economist at US investment fund Payden & Rygel, told the BBC that he expected the fiscal cliff to be avoided.
“I think we will get through the next couple of months, I think there will be some sort of deal or negotiation, and we will move onto a lower unemployment rate and stronger economic growth,” he said.
Business commentator Daniel Costello, managing director of financial advisory firm Titan Advisers, said it would be “extremely painful [for Americans] if these cuts were allowed to go through”.
However he thinks there will be some sort of compromise: “President Obama has privately and aggressively in recent months been pushing for what he is calling a grand bargain, which would be a compromise with the Republicans of some tax increases, but also cuts in entitlement [benefit] spending, particularly around healthcare.
“Republicans are weakened after this election… which has weakened Republican ability to counter some of President Obama’s wishes and demands around the fiscal cliff.”
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.
The US dollar fell slightly following the election result, with the euro rising to $1.286 from $1.281.
Analysts said the dollar had fallen because President Obama’s re-election means the Federal Reserve is likely to stick to its policy of quantitative easing (QE) – injecting fresh money into the US financial system.
QE is designed to boost lending, and therefore economic growth, but it can have a weakening effect on the currency.