Despite a decisive win over Republican Mitt Romney in Tuesday's election, Obama must negotiate with a Republican majority in the House of Representatives to try to overcome the partisan gridlock that gripped Washington for much of his first term.
The Democratic president's most immediate concern is the "fiscal cliff" of scheduled tax increases and spending cuts that could crush the U.S. economic recovery if it kicks in at the end of the year.
The prospect of Obama and Congress struggling to agree on the issue weighed heavily on global financial markets on Wednesday and helped send Wall Street stocks into a post-election swoon.
Obama also faces challenges abroad including the West's nuclear standoff with Iran, the civil war in Syria, the winding down of the war in Afghanistan and dealing with an increasingly assertive China.
At home, Obama's triumph could embolden him in his dealings with the Republicans, who were in disarray after failing to unseat him or reclaim control of the U.S. Senate, an outcome many conservatives had predicted. The party is now headed for a period of painful soul-searching.
Voters gave Obama a second chance despite stubbornly high unemployment and a weak economic recovery, but they preserved the status quo of divided government in Washington.
Obama's fellow Democrats retained control of the Senate and Republicans kept their majority in the House, giving them power to curb the president's legislative ambitions on everything from taxes to immigration reform.
This is the political reality facing Obama - who won a far narrower victory over Romney than his historic 2008 victory over John McCain when he became the country's first black president.
He returns to Washington later on Wednesday after basking in the glow of his re-election together with thousands of elated supporters at a victory rally in his hometown of Chicago in the early hours of the morning.
"We can seize this future together because we are not as divided as our politics suggests," Obama told the gathering.
Romney, a multimillionaire former private equity executive, came back from a series of campaign stumbles to fight a close battle after besting Obama in the first of three presidential debates.
But the former Massachusetts governor failed to convince voters of his argument that his business experience made him the best candidate to repair a weak U.S. economy.
CALL TO CONGRESS LEADERS
Trying to make good on his promise to seek compromise, Obama followed up in telephone calls with congressional leaders, including the two top Republican lawmakers, John Boehner and Mitch McConnell, to express his determination to work together.
"The president reiterated his commitment to finding bipartisan solutions to: reduce our deficit in a balanced way, cut taxes for middle-class families and small businesses and create jobs," a White House official said.
The problems that dogged Obama in his first term , which cast a long shadow over his 2008 campaign message of hope and change, still confront him. He must tackle the $1 trillion annual deficits, rein in the $16 trillion national debt and overhaul expensive social programs.
The most urgent focus for Obama and U.S. lawmakers will be to deal with the "fiscal cliff," a mix of tax increases and spending cuts due to extract some $600 billion from the economy at the end of the year, barring a deal with Congress. Economists warn it could push the United States back into recession.
House Majority Leader Boehner moved swiftly on the issue, citing "the need for both parties to find common ground and take steps together to help our economy grow and create jobs, which is critical to solving our debt.
Post-election concern about U.S. fiscal problems contributed to a fall in global financial markets as jittery investors scrambled for less-risky assets.
All three major U.S. stock indexes were down more than 2 percent by late afternoon, with the Dow Jones industrial average losing nearly 300 points and the S&P 500 on track for its biggest drop since June. Eurozone debt worries were also a factor in the market decline.
Boehner has made it clear he intends to stand firm against any income tax increases on wealthier Americans, which Obama has demanded.
Senate Republican leader McConnell gave no sign he was willing to concede his conservative principles.
"The voters have not endorsed the failures or excesses of the president's first term, they have simply given him more time to finish the job they asked him to do together with a Congress that restored balance to Washington after two years of one-party control," McConnell said.
COMFORTABLE WIN IN ELECTORAL COLLEGE
The nationwide popular vote in Tuesday's election was extremely close with Obama taking about 50 percent to 49 percent for Romney after a campaign in which the candidates and their party allies spent a combined $2 billion. But in the state-by-state system of electoral votes that decides the White House, Obama notched up a comfortable victory.
By early on Wednesday, he had 303 electoral votes, well over the 270 needed to win, to Romney's 206. Florida's close race was not yet declared, leaving its 29 electoral votes still to be claimed.
The Republican Party, after losing the past two presidential contests, is expected to analyze at length what went wrong and how to fix it, especially how it has alienated Hispanic voters who were an important constituency in Obama's victory.
Some critics have argued that the Republican party, with its conservative Tea Party faction, have moved too far from the American mainstream to attract enough independent voters to reclaim the White House.
"The fact is, Republicans are going to have to do a lot of rethinking at the presidential level," Newt Gingrich, a former House speaker who lost the Republican nominating race to Romney, told CBS's "This Morning" program.
Obama's win put to rest the prospect of wholesale repeal of his 2010 healthcare reform law.
Obama, who took office in 2009 as the ravages of the financial crisis were hitting the U.S. economy, must continue his efforts to ignite strong growth and recover from the worst downturn since the Great Depression of the 1930s. An uneven recovery has been showing some signs of strength but the country's jobless rate, at 7.9 percent, remains stubbornly high.
Obama may now reshuffle his cabinet. Treasury Secretary Timothy Geithner and Secretary of State Hillary Clinton plan to step down soon.
Democrats widened their control of the 100-member Senate by two. The Republican majority in the 435-member House means that Congress still faces a deep partisan divide.
"That means the same dynamic. That means the same people who couldn't figure out how to cut deals for the past three years," said Ethan Siegel, an analyst who tracks Washington politics for institutional investors.
International leaders offered Obama their congratulations. Israeli Prime Minister Benjamin Netanyahu, who has had a testy relationship with the U.S. leader, vowed to work with him "to ensure the interests that are vital for the security of Israel's citizens.
British Prime Minister David Cameron said Britain and the United States should make finding a way to solve the Syrian crisis a priority following Obama's re-election.
In the Middle East, where the Obama administration took a cautious approach while the Arab Spring shook the region, Obama's win prompted more of a sense of relief than happiness. A tweet from one of Saudi Arabia's most influential clerics summed up the Middle East's response. "Obama isn't good," tweeted Salman al-Oudah, "But he is the lesser evil."
(Reporting by staff in Washington and other bureaus; Editing by Alistair Bell)