* Obama dons work gloves for day of service projects
* Muted inauguration compared with 2009
* Obama to be sworn in Sunday, then again Monday
* Deficit, gun control, immigration are main challenges
By Mark Felsenthal and Jeff Mason
WASHINGTON, Jan 19 (Reuters) - President Barack Obama kicked off inauguration events for his second term on Saturday, rolling up his sleeves and joining in a nationwide day of community service projects honoring slain civil rights leader Martin Luther King Jr.
Obama will take the official oath of office in a private White House ceremony on Sunday, then have the pomp of a public swearing-in outside the U.S. Capitol Building on Monday - which falls on the national holiday marking King's birthday.
Launching the weekend's festivities, the president and first lady Michelle Obama took part in a National Day of Service, a volunteer program started when he took office four years ago as a way to pay tribute to King's legacy. They pitched in at the renovation of a local school.
Obama's second inauguration celebration will be a more muted affair than his historic swearing-in for his first term.
High unemployment and partisan fights over fiscal policies have drained some of the hope that marked Obama's first swearing-in after he swept to victory on a mantle of change in 2008 as America's first black president.
On Sunday, following a wreath-laying ceremony at Arlington National Cemetery, Obama will be sworn in officially at the White House at 11:55 a.m. EST (1655 GMT), meeting the constitutional requirement that he do so on Jan. 20. That portion will be private - except for a media presence - with a small audience of mostly family members.
Obama repeats the procedure the next day in the traditional open-air ceremony on a giant platform overlooking the National Mall.
Both times he will be sworn in by Supreme Court Justice John Roberts who, in 2009 after flubbing the oath the first time, administered it to Obama again in the White House the day after his inauguration.
It will be only the second time he has made an inaugural address, however, and millions worldwide will be watching. Some 800,000 people are expected to flock to Washington for the event, down from a record 1.8 million in 2009.
With workers rushing to complete preparations for Monday, the president and first lady Michelle Obama donned work gloves and helped varnish bookshelves at a local elementary school under renovation.
"This is what America is about. This is what we celebrate," Obama told a crowd of about 300 workers in the school gymnasium. He said the inauguration will be "a symbol of how our democracy works ... but it should also be an affirmation that we're all in this together."
Vice President Joe Biden, at the D.C. Armory helping to fill personal-care kits destined for overseas military service members, said of the administration's second-term agenda: "I think we're on the cusp of doing some really great things."
In his inaugural speech, Obama is expected to talk about the need for political compromise where possible - a nod to the divisive fights with the Republican-led House of Representatives over the "fiscal cliff" and raising the U.S. debt ceiling.
He will emphasize that the values on which the United States was founded should still guide the country in the 21st century and encourage Americans to make their voices heard to influence lawmakers' actions, according to an administration official.
He will also touch on the goals he hopes to address in his second term, while leaving detailed policy blueprints for his State of the Union address next month, the official said. Deficit reduction, gun control, immigration reform, and energy policy are likely to be top priorities in his second term.
Obama has been crafting his inaugural address for weeks, scrawling out drafts on yellow legal pads. This weekend, he faces the task of juggling speech preparations and his presidential duties, including briefings on the fate of Americans and others caught up in a still-unfolding hostage crisis at a desert gas plant in Algeria.
While second inauguration speeches rarely go down in history, Monday's address is a rare opportunity to face millions of television viewers and seek support for upcoming fights with the men and women who work in the Capitol building behind the podium where he will speak.
"This time it's scaled down, but it's still historic for all of America," said Courtney Prater, a construction worker visiting from Detroit, after a tour of the White House.
The White House views the two speeches - he delivers his State of the Union address before Congress on Feb. 12 - as two parts of a package, with the first one spelling out a vision and the second one specific policy proposals.
"The president, I think, is very appreciative of the fact that the American people have given him this opportunity to deliver a second inaugural address," White House spokesman Jay Carney told reporters this week.
"He believes that we have work to do, and he believes that both the agenda he has put forward so far and the agenda he will put forward in the future will help this country move forward in a variety of ways," Carney said.
After lambasting Republican opponent Mitt Romney during the presidential campaign for remarks that dismissed nearly half of the U.S. electorate, Obama is likely to offer some words of humility and resolve to represent even those who did not vote for him last year.
After the speech, Obama and the first lady will join Biden and his wife, Jill, at a luncheon at the capitol. Later the two couples will take part in the inaugural parade, returning to the White House in a motorcade and likely getting out to walk part of the way, waving at the crowd and surrounded by Secret Service members.
For weeks, workers have been building viewing stands along the parade route for visitors.
After seeing the rest of the parade from a spot in front of the White House, the Obamas will attend two official inaugural balls, dancing for the cameras and, in the first lady's case, donning a gown that will be scrutinized closely for its style and fashion sense.