* Faces tough decision on presidential run
* Many factors weigh in her favor
* State Dept. tenure transformed Clinton's public image
By Steve Holland
WASHINGTON, Jan 16 (Reuters) - In a matter of days, Hillary Clinton will leave the State Department behind and become a private citizen for the first time in 34 years. But her next big decision will be a very public one: whether to run for U.S. president in 2016.
Many factors would weigh in her favor should she decide to run. She leaves her Secretary of State job as the most popular member of Obama's Cabinet and the country's most admired woman - rated far ahead of even first lady Michelle Obama, according to a Gallup poll of Americans.
Plus, her party wants her. A Public Policy Polling survey found that 57 percent of Democrats would like her to run, compared to just 16 percent for another potential candidate, Vice President Joe Biden.
Her husband, former President Bill Clinton, has made no secret that he would love for her to seek the White House.
And yet Secretary Clinton seems to harbor doubts. She is recovering from a blood clot near her brain that befell her at the end of 2012. She will be 69 years old in 2016, a fairly advanced age for a president.
She would have to weigh whether she thinks Americans want four more years of Democratic rule in the White House, after President Barack Obama's eight years conclude in 2017.
And she seems to relish the idea of taking some time off, exiting the political stage, at least for a while. Running again would not only expose Clinton to the slings and arrows of political life once more, but also put at risk the reputation she has built as a loyal, hard-working, hard-nosed secretary of state. If she were to fail, part of her legacy would be as a two-time loser, after getting bested in the 2008 Democratic presidential race.
Clinton has been a public figure since entering the Arkansas governor's mansion in 1979 as first lady to Governor Bill Clinton. Since then, she's been America's first lady, a U.S. senator from New York, a presidential candidate who lost to Obama, and since 2009, the globetrotting top U.S. diplomat.
She's offered only a few clues as to what could lie in her future, none of them definitive.
"I think after 20 years -- and it will be 20 years -- of being on the high wire of American politics and all of the challenges that come with that, it would be probably a good idea to just find out how tired I am," she told a town hall event last year.
Will she be going into retirement?
"I don't know that that's the word I would use, but certainly stepping off the very fast track for a little while," Clinton told reporters last week when she returned to work after recovering from the blood clot.
'NEVER SAY NEVER'
Associates of Clinton say her position now is that she is not going to run. But they are not sure if this decision is final or whether she will try again to become America's first woman president.
"I don't think she wants to run," said a former aide. "But I think after taking a break, after doing something else, I think that could change. You never say never."
Another former staffer, having watched how hard Clinton campaigned in 2008, has doubts about whether she would expose herself to another brutal campaign. Clinton had been the clear front-runner, but her staff and organizational woes helped the relatively unknown Obama to beat her.
"There's a time and place for things in life and that last campaign was brutal and she gave it her best shot and she really is exhausted. She may be coming to the recognition that there are other ways to do public service. You can sometimes get more done out of government than in government," the staffer said on condition of anonymity.
As Secretary of State, Clinton has kept a punishing schedule, breaking travel records and visiting 112 countries.
After a period of rest, Clinton is likely to start doing some foundation work on behalf of women and children, a priority of hers since her days in Arkansas. Whether this initiative would be part of her husband's Clinton Foundation or a separate Hillary Clinton foundation is unclear.
While some candidates spend four years running for president, a Clinton decision to seek the presidency could come fairly late in the process, given her popularity within the party and her husband's lengthy list of potential donors who could help her mount a campaign quickly, Democrats say.
But a late announcement of her candidacy could also freeze the 2016 Democratic nomination battle, dissuading other Democrats from jumping in until Clinton's plans were clear.
Bob Shrum, who was campaign manager for Democratic presidential nominee John Kerry in 2004, said Clinton would have no trouble assembling an A-list campaign staff.
"I don't think the question for her would be who," said Shrum. "The question would be which of the many people she wants to move with. There's a whole plethora of really talented people who want to move with her."
Bill Clinton remains enormously popular, but whether Americans would want the former president, who was impeached over an affair with an intern, back in the White House in 2017 remains to be seen.
ONCE SCORNED, NOW FEARED
Clinton's time in the public eye as secretary of state has allowed her to shed an image as a politically polarizing figure, one who as U.S. first lady railed against a "vast right-wing conspiracy" out to get her husband and who was responsible for a health care policy debacle.
Some conservative Republicans have gone from scorning her to fearing her. If Clinton runs in 2015, "The Republican Party is incapable of competing at that level," former House of Representatives Speaker Newt Gingrich said last month.
Clinton has earned plaudits from Democrats and Republicans alike for her handling of U.S. foreign policy.
And yet her last months at the State Department have not been without controversy and some issues could return to haunt her during a presidential campaign.
The deaths of four Americans killed by Islamic militants last Sept. 11 at the U.S. mission in Benghazi, Libya, occurred under her watch, amid questions about whether they had been provided with adequate security. Among the dead was Ambassador Chris Stevens, the first U.S. ambassador to die in office since 1988.
An internal probe absolved Clinton of any responsibility. She is due to testify on Jan. 23 before the House Foreign Affairs Committee, after postponing her testimony due to illness.
The secretary of state's concussion has raised some questions about her health that would have to be resolved, along with her tendency toward secrecy.
Clinton returned from a European tour on Dec. 7 suffering from a stomach virus, forcing her to postpone a Middle East trip. On Dec. 15, the State Department announced she had become dehydrated, fainted and suffered a concussion.
But the initial State Department statement did not say exactly what day she sustained the concussion or exactly where she was when it happened. By contrast, when President George W. Bush had a choking episode involving a pretzel in 2002, reporters knew within hours the exact circumstances.
Experts believe Clinton, should she run, will have to put out a detailed medical report as proof that she is fit to be commander in chief.
"Any candidate of a certain age is going to have lots of questions about their health," said David Yepsen, director of the Paul Simon Public Policy Institute at the University of Southern Illinois. "That's going to be a hurdle for her to overcome if she's going to run."