"There are two arguments in this," said Lucia Newman, Al Jazeera's Latin American correspondent.
"One is that it's better to let things get worse before they get better, and clean the house within the coalition parties - even if that means having to live with a conservative government for one or two political terms.
"The other is that it is a very dangerous proposition. Once you let the right-wing in, it's very hard to get them out again, and that its better to transform the coalition from within - something that hasn't really happened over the last 20 years."
But support for the two trailing left-wing candidates wanting to continue Bachelet's economically successful policies in the prosperous copper-producing nation is strong enough to make a January 17 run-off appear likely.
The outcome of the vote promises to be close, largely because left-wing ballots split in Sunday's first round of the election will be combined in the second round behind just one candidate.
Currently Eduardo Frei, a 67-year-old former president, and Marco Enriquez-Ominami, a 36-year-old independent and former film director, are battling it out on Sunday for the right to face Pinera in January.
While Frei, who held power between 1994 and 2000, has 31 per cent going into Sunday's election, and MEO, as Enriquez-Ominami is known, just 18 per cent.
Uncertainties as to how Chilean youths will vote, and MEO's charisma, mean either could yet emerge as the left's champion.
The split leaves the left weakened and has handed Pinera - who has interests in television, Chile's big airline LAN and a football club - an unprecedented chance.
A run-off duel between the current two leading candidates could see Pinera triumph with 49 per cent of the vote to 32 per cent for Frei, according to the latest surveys.
"These are the best conditions ever for the right to win the presidential election," said Carlos Huneeus, the head of the Public Studies Center (CERC) that conducted the most recent surveys of voters' intentions.
"I don't exclude the possibility of it winning in the first round," he added.
But Jose Antonio Gomez, a spokesman for Bachelet's outgoing government, which will be replaced after elections in March next year, said the left's support "could rise and we are sure that we will win in the second round".
Analysts said the ruling Concertacion left-wing coalition might have worn out its welcome after winning the past four successive elections.
"That feeling of tiredness is completely normal because of the cumbersomeness of the Chilean electoral system, which doesn't allow minority representation and favours the same old political figures," said Mauricio Morales of the Social Sciences Institute of Chile's Diego Portales University.