NEW YORK, July 3 (Reuters) - Colombian President Alvaro Uribe was greeted with cheers, folk dancers and banners clamoring for his re-election when he stepped off a helicopter for a community meeting in Colombia last month.

After Wednesday's spectacular rescue of FARC hostage Ingrid Betancourt and three Americans, the U.S. ally may have gained even more support to run for a third term if he wants, with admirers saying he is the man to take on the Marxist rebels.

Already hugely popular because of his U.S.-backed crackdown on the FARC guerrillas, Uribe has been cagey about whether he is mulling seeking re-election. But the idea of a third term is worrying critics concerned about democracy and even some on Wall Street, which has openly backed him.

Uribe recently pushed the idea of a vote on to the agenda by calling for a referendum on re-running his 2006 re-election after a court found the vote may have been tainted by corruption.

Foes worry he will use his popularity to muscle through a vote and bypass the country's institutions.

They say a re-run of the 2006 election -- while touted as strictly to confirm the legitimacy of that vote -- would promote acceptance of him staying in power if supporters managed to push through a constitutional reform removing a ban on a third successive term.

"The temptation, of course, will be to parlay that surge in popularity into support for the proposed referendum on new elections," said Cynthia Arnson at the Woodrow Wilson center.

"Even Colombians supportive of Uribe have questioned the idea of a third term, and the danger is that presidential hubris will ride roughshod over Colombia's judiciary and political institutions."

Uribe, a studious-looking attorney first elected in 2002, is known for his tough work ethic and unflinching opposition to the FARC rebels who killed his father, says he will only run again in case of "disaster." He says he wants to keep alive his "Democratic Security" policy to help drive back rebels and draw in more foreign investment.

His re-election in 2006 followed a contested reform of the constitution to allow a second term.

Supporters are now collecting signatures to change the constitution again. A referendum proposal on such a change would have to be reviewed by Congress and by the Constitutional Court before a vote.

TWO PATHS AHEAD

Uribe, who turns 56 on Friday, has been put on the defensive by the scandal over the 2006 re-election and probes into more than 60 lawmakers for ties to former paramilitary death squads who carried out massacres before handing in their weapons under a peace deal with his government.

But with the Andean country's economy growing strong and more Colombians able to travel freely in a country where illegal armed groups once roamed at will, Uribe's popularity is soaring at around 80 percent, according to a recent poll.

For opponents, everything points to a consolidation of authority by a president they say already uses his high popularity to bully the country's institutions.

"The president can choose one of two paths: stay in power, because no one is going to contradict him, or finish his second term and go down in history as the man who brought the FARC to its knees," said opposition lawmaker Gustavo Petro.

Still, critics who question his government's human rights record cannot cast doubt on his government's success in dealing blow after blow to Latin America's oldest leftist insurgency.

Once a mighty force of 17,000 fighters able to choke off cities, set bombs in upscale neighborhoods and kidnap at will, the Revolutionary Armed Forces of Colombia or FARC has been reduced to around 9,000 combatants.

The guerrillas have lost three top commanders this year and hundreds have deserted from its ranks prompted by military pressure and government rewards.

Betancourt, a former senator kidnapped during her own presidential election campaign in 2002, appeared to back a Uribe re-election.

"I have always been in favor of re-elections perhaps I have been influenced by French democracy, where the concept of re-election exists," Betancourt, a dual French-Colombian citizen, said after her release without giving more details.

But Wall Street, which has applauded Uribe's investment policies, has been skittish over another constitutional reform to allow Uribe's re-election.

Several Uribe allies are touted as possible candidates and opposition parties talk about a loose alliance to counter a new Uribe run. Still, no clear alternative candidates have emerged. Some experts believe Uribe is keeping his cards close to his chest to avoid becoming a lame duck in the waning two years of his second term.

"It would be good to have someone that is not Uribe carrying on the same policies for that would be a great sign of institutional maturity," said Alberto Ramos at Goldman Sachs.

"If there is no one out there to carry on successfully the same policies, an eventual third term by Uribe would be the best second-best alternative for it would guarantee no policy reversal," he said.

Even before the rescue of the hostages, there was no doubt in the minds of hardcore Uribe supporters such as Isidora Julio, who are already calling for him to rewrite the constitution to be able to run again.

"He's the only one who wears the pants," she said at one of Uribe's weekly town hall meetings where supporters flock to hear him manage problems such as building roads and schools. "Now we can go anywhere without fear."