Yesterday, Jan. 10, was the day when Hugo Chávez was scheduled to be sworn in for the fourth time as Venezuela’s president. Instead, he is lying in a Cuban hospital, suffering serious complications from cancer surgery, and the country’s legislature, dominated by the president’s loyalists, has delayed the ceremony indefinitely. As Venezuelans grapple with the political uncertainty created by Chávez’s precarious health, the prospect of a post-Chávez era poses complex choices for a number of other countries, not least among them, the United States.

During almost 14 years in office, Chávez made anti-Americanism the cornerstone of his foreign policy, working at every step to antagonize U.S. goals and undermine Washington’s influence. Perhaps the greatest irritant of all was the close relationship he forged with Iran, a country the U.S. and its allies believe is trying to develop nuclear weapons and sponsoring international terrorism.

As the U.S. spearheaded efforts to pass United Nations sanctions to stop Iran’s nuclear enrichment, Chávez traveled to Tehran and, along with Iranian President Mahmoud Ahmadinejad, provocatively announced the creation of what they called an “Axis of Unity” against the U.S. The two countries work together in a number of areas. Of particular interest to the U.S. is Venezuela’s help to Iran in circumventing international sanctions.

The question for Washington now is how to maximize the chances that once Chávez leaves the scene, the ties linking Caracas and Tehran, more than 7,000 miles away, will fade.

Just before the end of the year, President Barack Obama signed into law the Countering Iran in the Western Hemisphere Act, which instructs the State Department to develop a strategy to “address Iran’s growing hostile presence and activity” in Latin America, and directs the Department of Homeland Security to take measures to protect U.S. borders with Mexico and Canada to keep out “operatives from Iran... Hezbollah or any other terrorist organizations.”

For Iran and its Lebanese ally Hezbollah, Chávez’s worsening condition could not come at a worse time. Their closest and most crucial ally, Syrian President Bashar al-Assad, is engulfed in a brutal civil war, likely to put an end to his regime and possibly destroy Syria’s ties with Iran and Hezbollah.

The headwinds they face in Latin America recently came up in a speech by none other than Hezbollah leader Hassan Nasrallah. Speaking a couple of days after the start of the year, Nasrallah said 2013 would bring a “very dangerous phase” for his organization, citing efforts to add the group to the European Union’s terrorist list and to restrict its movements in Latin America as specific challenges.

Before traveling to Cuba for his most recent cancer surgery, Chávez dramatically acknowledged he may not be able to remain in power and anointed Vice President Nicolas Maduro as his chosen successor.

Washington has already taken tentative steps, seeking to reach out to Maduro -- as has Tehran. It is not exactly clear what the American strategy is, but there is no indication that the first moves were effective or well-received.

The U.S. said that a telephone conversation between Maduro and a top State Department official, Roberta Jacobson, was aimed at improving relations, and there have been reports of other bilateral contacts.

However, Maduro lashed out at reports that relations with Washington would improve after Chávez dies, calling it a distortion and manipulation by Washington.

At about the same time, Iranian media reported a telephone call between Maduro and Ahmadinejad. The two are already friends. Maduro has strong connections with Tehran, having met in person with top officials on many occasions during visits to Iran and having served as their host when they traveled to Venezuela. Maduro is a favorite to succeed Chávez in both Tehran and Havana, not to mention Caracas.

The Venezuelan constitution says if the president dies or cannot take office, the head of the National Assembly would take power temporarily. That position is held by another Chávez loyalist, Diosdado Cabello. After 30 days, a new election would take place. Cabello and Maduro are just two of several Chávez supporters who would vie for power in the factional power struggles to succeed the iconic president.

Chávez’s unqualified blessing means that for now Maduro is the country’s most powerful man. He would benefit from an initial surge of support. And there is no question he and the Chavista forces have a firm grip on all the institutions of power. Chávez’s entrenched United Socialist Party of Venezuela (PSUV) will not crumble without its leader.

And yet, there is no denying that Chavismo thrived because of Chávez. There is no guarantee it will survive without him in the long term, especially in the face of daunting economic problems, beginning with a budget deficit that stands at an astonishing 20 percent of GDP.

For Washington, this means that forging ties with Maduro risks strengthening him against his rivals, helping him quash internal rivals and legitimize his rule at a time when it is unclear just how closely he and other Chavistas plan to follow the constitution.

Infighting within the ruling party’s ranks, and the lack of a candidate with strong personal appeal, could open the way for the opposition.

Opposition leader Henrique Capriles, who mounted a strong campaign against Chávez in last October’s presidential election, is on record saying he would bring a dramatic change in foreign policy, ending arms purchases from Russia, pulling away from China, reviewing oil deals that strengthen other authoritarian regimes in Latin America -- and rethinking controversial links with Iran.

Washington would do well to keep conversations at the lowest possible volume, whether with the opposition or other would-be Chávez successors, while openly urging Venezuela to abide by democratic norms. If, in the event Chávez is unable to serve his term for whatever reason, a fair contest is allowed and enough time passes to loosen the emotional power of grief, the Venezuelan people may wake up to the dismal state of their economy, and discover there are better ways to decrease poverty and build lasting prosperity than Chavismo.

A close relationship between Iran and Venezuela has always been a geographic and diplomatic oddity, one made possible only because of Chávez’s own worldview. Chávez’s immediate successor will seek to maintain it, but the intensity and impact will be difficult to preserve for long in a post-Chávez Venezuela.

Frida Ghitis is an independent commentator on world affairs and a World Politics Review contributing editor. Her weekly WPR column, World Citizen, appears every Thursday.