WASHINGTON (Reuters) - President Barack Obama had little time to savor victory on Wednesday after voters gave him a second term in the White House where he faces urgent economic challenges, a looming fiscal showdown and a still-divided Congress able to block his every move.

U.S. President Barack Obama, first lady Michelle Obama and their daughters Malia and Sasha (L) walk from Marine One to Air Force One in Chicago, November 7, 2012 following the U.S. presidential election. The first family are returning to Washington following Obama's second term win. REUTERS/Jason Reed

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 start of next 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. Their 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 headed back to Washington 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.

Before leaving Chicago, he visited his downtown campaign headquarters to thank staff and volunteers.

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 starting early next year, barring a deal with Congress. Economists warn it could push the United States back into recession.

Obama has pledged to increase tax rates on Americans earning more than $250,000 as a part of his “balanced approach” to deficit reduction - something Republicans still vow to resist.

In remarks to reporters, House Speaker Boehner struck a conciliatory tone but stuck to the Republican position that they will consider boosting revenues to help reduce deficits, but only as a “byproduct” of tax reform that lowers rates and eliminates loopholes and deductions.

Boehner said lawmakers and Obama should find a short-term solution to avoid the fiscal cliff and work on a long-term debt reduction plan in 2013.

“In order to garner Republican support for new revenues, the president must be willing to reduce spending and shore up the entitlement programs that are the primary drivers of our debt,” Boehner said.

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.

Vice President Joe Biden told reporters the election delivered a mandate on moving closer to the administration’s views on tax policy, and Republicans would have to do some “soul-searching” about issues they would be willing to compromise on, according to a pool report.

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 fell more than 2 percent, with the Dow Jones industrial average losing more than 300 points and the S&P 500 posting its biggest drop since June. Euro zone debt worries were also a factor in the market decline.

COMFORTABLE WIN IN ELECTORAL COLLEGE

The nationwide popular vote in Tuesday’s election was extremely close with Obama taking about 50 percent to 48 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 late 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.