By Alexandra Ulmer
SANTIAGO (Reuters) - When Michelle Bachelet became health minister under President Ricardo Lagos in 2000, he assigned her a daunting task: end the long lines in Chile's saturated primary health care centres within three months.
Bachelet struggled to meet the deadline. Yet, when Lagos visited a medical centre to survey the situation, a woman whisked him aside to praise Bachelet and beg him to keep her in his cabinet.
"I can't remember ever being told during my presidency not to get rid of a minister," a chuckling Lagos, who governed from 2000 to 2006, told Reuters in an interview. "Within a short period of time, Bachelet managed to forge a relationship with people. She's seen by some as the mother of all Chileans."
The paediatrician-turned-politician's efforts to improve health care and her warm style paved the way for her to succeed Lagos in office as Chile's first female president from 2006 to 2010.
And that same charisma, coupled with more ambitious policies to bridge steep economic inequality, is poised to hand the 62-year-old centre-left politician a second term in the La Moneda palace.
Bachelet fell just short of the 50 percent of votes needed for victory in the first round of Chile's presidential election on Sunday. Still, she won more than 46 percent support and is seen handily beating her main rival, the conservative Evelyn Matthei, in a runoff between the two on December 15.
Matthei won about 25 percent of the vote on Sunday.
A victim of torture under the dictatorship of General Augusto Pinochet and a single mother of three, Bachelet was one of conservative Chile's most unusual presidents since its return to democracy in 1990.
She is beloved by many lower and middle class women disenchanted with the political elite in Chile, which boasts stability and growth but also has the worst income inequality of the 34 counties in the Organisation for Economic Cooperation and Development.
Critics say her popularity is too anchored in her personality, and many leftists disillusioned with her moderate record of reform while in power the first time are sceptical of her fresh batch of promises.
She vows a reform blitz that includes hiking corporate taxes to fund an education overhaul, overhauling the Pinochet-era constitution and legalizing abortion in some circumstances.
Many who feel marginalized from what has been called Latin America's shining economic success story are pinning their hopes on her.
Far from the gleaming skyscrapers and polished parks of affluent eastern Santiago, euphoric supporters in the low-income neighbourhood of Cerrillos greeted Bachelet last week.
They fervently waved flags emblazed with a big, simple 'M' as Bachelet rode in to the tune of her jingle 'Chile de todos,' or 'Chile for all', blasting from nearby speakers.
"She's a fighter. It's what I value most," said Josefina Osorio, a 32-year old law student, shouting above the cheers. "She's back with new ideas."
Barred constitutionally from running for re-election at the end of her first term, Bachelet moved to New York to head U.N. Women, an agency aimed at improving the lives of women and girls.
Displaying her common touch, Bachelet said in an interview that one of the things she most enjoyed about living away from Chile was the freedom to go food shopping in Bermuda shorts. During the same program she danced with a popular television host to the rhythm of cumbia, a Colombian music genre popular throughout Latin America.
"She puts forth a social ideology rather than a political one," said political analyst Guillermo Holzmann. "There's no logical or theoretical explanation (for her appeal)."
TORTURE, EXILE, MEDICINE
Some of her appeal stems from her life story.
As a young leftist, Bachelet's life was deeply marked by the coup that overthrew President Salvador Allende in 1973 and ushered in the brutal 17-year Pinochet rule.
Bachelet's father, an air force general loyal to Allende, was arrested the day of the coup and later tortured by Pinochet's agents. He died in prison in 1974.
The following year, two secret police officers burst into the flat where Bachelet and her mother lived. The women were whisked away blindfolded to Villa Grimaldi, an infamous military-run centre on the outskirts of Santiago where they were tortured.
Once freed, she and her mother fled to Australia and later on to what was then East Germany. She returned to Chile in 1979.
In an astounding twist, Matthei is also the daughter of an air force general - but one who went on to be part of the Pinochet junta.
The two generals were friends in the years before the coup and their daughters played together as kids. Bachelet said she spontaneously called former general Fernando Matthei "uncle," a common term of endearment in Chile, when she saw him again recently.
Still, Bachelet's affable nature irks some.
"Everything she says is ambiguous. Sure, we all want more justice, more love but ..." said David Altman, a political scientist at the Universidad Catolica. "She doesn't gamble when you have to gamble. She creates a commission for anything."
Critics point to her government's slow response to a devastating 8.8-magnitude earthquake that hit at the very end of her term in 2010. The navy's catastrophe-alert system failed to warn of the ensuing tsunami, leaving hundreds who survived the quake to be killed by massive waves.
Many in Chile also question why Bachelet did not implement the policies she is now championing.
Presidential candidate Marco Enriquez-Ominami, a left-leaning economist and filmmaker who wooed some of the youth vote away from Bachelet, says she "copied" his ideas, and in his campaign he called on Chileans to "vote for the original."
Another weak point is that Bachelet is not close with most political parties due to her time in exile and the fact she was never a member of Congress, Holzmann says.
That could prove tricky as deft management of a notoriously challenging Congress will be crucial to ensure passage of her flagship reforms. And expectations are sky-high.
"More than anything I want free education. It's what I most long for, because I have grandkids," said Marta Monica Ramirez Tobar, a 65-year-old former shopkeeper in Cerrillos. "It wasn't possible for my own kids, but it is for my grandkids."
(Reporting by Alexandra Ulmer; Editing by Kieran Murray and Jackie Frank)