Singing folk songs and strumming the guitar at his campaign rallies, Hugo Chavez shows no sign that he's facing the strongest challenge to his 13-year rule in Venezuela.

He has dismissed his much younger challenger, Henrique Capriles Radonski, as a "fly" not worth chasing, when challenged to a debate earlier this year.

Chavez's opponents are confident that this Sunday, Capriles will unseat the long-ruling leftist leader, a refrain previously heard before eventual defeats.

Yet the incumbent is a political survivor and remains popular at home. But there are signals, observers say, that this time Chavez really is on the ropes.

Chavez's influence over Latin America's left-leaning governments has often rankled the United States, Venezuela's largest trading partner. Venezuela is the fourth-largest exporter of oil to the United States. Despite that tight economic relationship, the two countries are not exactly close allies: Chavez often rails against the U.S. and its allies as "imperialists."

Further complicating the U.S.-Venezuela relationship, Chavez is allied with Iran's Mahmoud Ahmadinejad, he defended former Libyan leader Moammar Gadhafi and he has even offered his support for Syria's leader Bashar al-Assad.

At stake for Venezuelans is the ideological trajectory of their country.

Chavez, 58, has had more than a decade to implement his vision of 21st century socialism, a view that emphasizes use of state oil windfalls to fund social programs.

Observers say Capriles, 40, represents a moderate alternative.

He has vowed not end the social programs that Chavez has set up, and he promises to fight corruption that has grown in the public sector.

The candidates offer two distinct paths to solve the problems that are on Venezuelans minds: decaying infrastructure, high crime rates and political polarization.

A close race?

As expected, both sides claim they will be victorious -- and both sides have polls to back up those claims.

Several polls gave Chavez a double-digit lead, while at least one gave Capriles a narrow lead. Chavez supporters say the majority of polls were clear. Those supporting Capriles say people were afraid to voice their real opinions.

"The information we get from the polls is, at best, confusing," said Federico Welsch, a political analyst and retired professor at Universidad Simon Bolivar.

Part of the problem is "an inherent bias in polling companies," according to Inaki Sagarzazu, a Venezuelan professor of politics at the University of Glasgow in Scotland, who has taken a closer look at the pollsters.

Capriles, he noted, also must believe it is a close race, as evidenced by a speech this summer in which he spoke directly to the military, assuring them and other institutions that things will be OK if he wins.

That address was significant because questions exist about whether the military, whose leadership ranks is stacked with Chavez loyalists, will accept a defeat.

Controlling for biases, there are two conclusions that Sagarzazu has drawn from the polls: That Chavez is "stuck" with support near -- but not quite at -- 50%, and that Capriles is closing the gap.

"We're looking at a long night on October 7 because things look closer than polls or the government make it seem," he said.

Chavez, cool and hip

New campaign posters for Chavez have featured him popping a wheelie on a motorcycle, playing basketball and even performing as a rap artist.

It's a sharp contrast with the image of a sick man who was diagnosed with cancer last year and underwent two surgeries, in addition to multiple rounds of chemotherapy and radiation treatments.

The image makeover is part of an effort to capture support for Chavez among Venezuela's undecided voters -- mostly young people -- who make up 23% of the electorate and could play a pivotal role in Sunday's election.

Neither Chavez nor anyone in his government have publicly discussed what kind of cancer he has. He recently objected to a reporter's question about his health.