* Short private ceremony at White House
* "You didn't mess up," daughter tells him
* Obama will do it again in public event Monday
* Less excitement for second inauguration than 2009 event
* Country's mood tempered by economic and political woes
WASHINGTON, Jan 20 (Reuters) - President Barack Obama took the official oath for his second term on Sunday at the White House in a small, private ceremony that set a more subdued tone compared to the historic start of his presidency four years ago.
Gathered with his family in the Blue Room on the White House's ceremonial main floor, Obama put his hand on a family Bible and recited the 35-word oath that was read out loud by U.S. Chief Justice John Roberts.
"I did it," Obama said as he hugged his wife, Michelle, and daughters Sasha and Malia. "Thank you, sweetie," he told Michelle when she congratulated him. "Good job, Dad. You didn't mess up," 11-year-old Sasha Obama told her father.
It was a low-key start to the first African-American U.S. president's second term, which is likely to be dominated - at least at the start - by budget fights with Republicans and attempts to reform gun control and immigration laws.
Obama, 51, will be sworn in publicly on Monday outside the West Front of the Capitol overlooking the National Mall in front of as many as 800,000 people, a much bigger ceremony replete with a major address and a parade.
Downtown Washington was all but locked down with heavy security. Many streets were closed, lined with barricades. Police sirens blared. Outside the White House on Pennsylvania Avenue, an elaborate presidential viewing stand encased in bullet-proof glass was set up for Obama and other VIPs to watch the parade.
Sunday's ceremony, shown live on television, was needed because the U.S. Constitution mandates that the president take office on Jan. 20. Planners opted to go with a private ceremony on the actual date and then hold the ceremonial inaugural activities the next day.
By Monday, Obama will have been sworn in four times, two for each term, putting him equal to Franklin Roosevelt, who won four terms. A second Obama swearing-in was deemed necessary in 2009 when Roberts flubbed the first one. On Sunday, Roberts read the oath carefully from a card and there were no mistakes.
Obama, who won a second four years on Nov. 6 by defeating Republican Mitt Romney after a bitter campaign, opens round two facing many of the same problems that dogged his first term: persistently high unemployment, crushing government debt and a deep partisan divide over how to solve the issues.
This has taken some of the euphoria out of his second inauguration, with TV pundits debating how successful he will be and whether he can avoid policy over-reaching that often afflicts two-term presidents.
If the president harbored any doubts himself, there was no sign of it as he attended a rousing service at Metropolitan African Methodist Episcopal Church in downtown Washington where he and Michelle, who is sporting a new hair style featuring bangs, clapped and swayed to gospel music.
"Forward, forward," shouted Reverend Ronald Braxton to his congregation, echoing an Obama election campaign slogan.
Early Sunday morning, Vice President Joe Biden was sworn in by Supreme Court Justice Sonia Sotomayor, making her the first Hispanic judge to administer an oath of office for one of the nation's two highest offices.
Obama and Biden then joined forces to lay a wreath of flowers at the Tomb of the Unknowns at Arlington National Cemetery in a solemn remembrance of those killed in the line of duty.
Biden's family, about 120 guests and a few reporters witnessed the private swearing-in ceremony in the main foyer of his Naval Observatory residence. Biden used a Bible with a Celtic cross on the cover that has been in his family since 1893.
The audience for Monday's ceremony is not expected to be as big as in 2009 when a record 1.8 million people crammed into the National Mall to witness the swearing-in. Turnout is projected at 600,000 to 800,000, with millions more watching on television.
INAUGURAL ADDRESS IS CENTERPIECE
Obama's Inauguration Day speech will set the tone for the start of his second term and gives him a chance to lay out his vision on where he would like to lead the country. He has been drafting the speech on yellow legal pads and working with his speech writers.
Senior Obama adviser David Plouffe told CNN that Obama would talk about how "our political system doesn't require us to resolve all of our disputes or settle all of our differences," but that it does encourage common ground.
"I think it's going to be a hopeful speech," Plouffe said.
Lately the president has been using a more combative tone against his Republican opponents, a possible foreshadowing of a more aggressive effort at trying to get his way.
After his tumultuous first term during which he achieved an overhaul of the U.S. healthcare system, his second term opens in the midst of a feud with congressional Republicans over taxes and spending.
His top policy goals for the first year, so far, include tightening gun regulations in response to the massacre of 20 children and six adults at a Connecticut elementary school a month ago. Obama is also seeking an overhaul of immigration laws and tax reform.
Abroad, he is facing a challenge from a resurgence of Islamist extremists in North Africa exemplified by the recent hostage-taking that turned deadly at an oil facility in Algeria. He is also winding down the war in Afghanistan and dealing with Iran's nuclear ambitions.
Obama will save specific policy proposals for his annual State of the Union speech before Congress on Feb. 12.
In his inaugural address, Obama is expected to talk about the need for political compromise where possible, a reminder of the intense battles in his first term that led to paralysis and dysfunction in Washington.
"It'd be great if the inauguration were a unifying moment - though I honestly can't say it will be. But just maybe for a day they can bury the hatchet and celebrate an important day for American democracy," said Brian Hurley, 57, a local salesman, as he guided an out-of-town visitor outside the White House gates.
With the public ceremony falling on the national holiday honoring slain civil rights leader Martin Luther King Jr., Obama will also have a chance to draw historic parallels. While taking the oath on Monday, he will place his left hand on two Bibles - one once owned by Abraham Lincoln and the other by King.
The Obamas will attend two official inaugural balls - compared to the 10 that were held in 2009.