RPT-Hillary Clinton leaving world stage, but for how long?

* Faces tough decision on presidential run

* Many factors weigh in her favor

* State Dept. tenure transformed Clinton's public image

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.

Cl! inton 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! governme! nt," 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 f! rom scorn! ing 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 thei! r 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."