What might Obama's legacy be after 4 more years?

As jubilant Democrats celebrated the re-election of Barack Obama at his Chicago victory party, talk quickly turned to how the U.S. president's legacy hinges on his next four years in office — and how compromise will be crucial in approaching issues ranging from avoiding another recession to taking the lead on climate change.

The struggling U.S. economy has been the dominating election issue and was chief on most voters' minds, according to exit polls. But Obama, in his victory speech early Wednesday, gave some indications of where he wants his second term to head beyond the recovery.

In a lofty address, he appealed for compromise with Republicans, saying he was willing to work with them to reduce the federal deficit and the country's dependence on foreign oil, as well as reform the tax code and fix the immigration system.

The president also made a passing reference to the dangers of climate change, an issue that was barely mentioned in the campaign's earlier months until it roared back into the spotlight in the final days with superstorm Sandy's recent devastation of the coastlines of the U.S. northeast states.

"We want our children to live in an America that isn't burdened by debt, that isn't weakened by inequality, that isn't threatened by the destructive power of a warming planet," Obama said.Republican presidential candidate Mitt Romney delivers his concession speech at his election night rally in Boston early Wednesday. (Brian Snyder/Reuters)

Speaking ahead of the president in his later-than-expected concession speech, defeated Republican nominee Mitt Romney made his own appeal for co-operation from both sides.

"At a time like this, we can't risk partisan bickering and political posturing," he said. "Our leaders have to reach across the aisle to do the people's work, and we citizens also have to rise to the occasion."

But several volunteers and supporters attending Obama's victory bash said they now want the president to use his new mandate to go further, such as tackling climate change head-on or finding a peaceful solution to the impasse with Iran on its nuclear program.

Breakthough on immigration?

With a broader mandate than expected from Tuesday's win, Obama also has the chance to shape and leave a legacy not just for himself, but also for his party, through the election's connection with new constituencies that seem to be forming.

One obvious group would be Latinos, who overwhelmingly supported Obama at voting booths.

Polls have indicated a large majority of the Latino community favours immigration reform that would give some path toward permanent residency to the more than 12 million undocumented immigrants who already live and work in the United States.

Republicans, perhaps looking at how badly they fared among Hispanic voters in the presidential race this time around, could be willing to work to find common ground, despite past bipartisan attempts ending in failure and bitter recriminations.

At the Obama celebration in Chicago, supporter Angie Vaca said she wants the president to make immigration reform his top priority to help people "who love this country and live in fear of being pulled away from their dream."

"We're tired of waiting," Vaca, 30, a nurse and U.S.-born Latina, told CBCNews.ca.

Congress still gridlocked?

Despite the conciliatory words from the two candidates, when the dust settled, Republicans still retained control of the House of Representatives, and the Democrats will hold on to the majority in the Senate.

Supporters cheer at the end of President Barack Obama's remarks during an election night party in Chicago. (Matt Rourke/Associated Press)

That leaves the structure of the partisan gridlock in Congress that plagued the last two years of Obama's first term essentially intact, meaning he may again find himself limited in what he can accomplish when the new members take office in January.

"I'm not optimistic for a lot of healing coming out of this election," Roger Simon, chief political columnist of Politico, told CBC News on Tuesday before the results came in.

In Simon's eyes, the U.S. has entered a deep period of hyper-partisanship that has created a paralysis in Congress that shows no signs of dissipating.

"Congress is a place where hope goes to die," Simon said bluntly.

Fiscal cliff, Iran loom as challenges

Even before Obama's second term technically begins in January, he faces immediate short-term challenges, including high unemployment, slow growth and the country's latest "fiscal cliff" of a budget crisis — this time, a set of already legislated federal spending cuts totalling $600 billion US with higher taxes caused by the expiration of tax cuts brought in by Obama's predecessor, George W. Bush, coming down the pipe during the month.

If no budget deal is reached by the end of the year, world markets could panic as they did in previous U.S. fiscal showdowns, further threatening the country's economic recovery and possibly triggering another global economic crisis.

Also looming is the threat of a nuclear-armed Iran and Israel pressing Obama for a so-called "red line," or threshold that would determine when both the United States and Israel would take military action against Iran's nuclear enrichment sites.