The official death toll from the Friday's 7.5 quake and tsunami that struck the west coast of Sulawesi island has surged to 1,407 but there are fears it will rise when the full scale of destruction is determined and the missing are accounted for.
Widodo, a former furniture businessman and the first president to come from outside the political or military establishment, will seek another five-year term in the April 17 election.
A quietly spoken reformer, he has enjoyed strong popularity but faces hostility from conservative nationalist and Islamist forces in the predominantly Muslim country of 260 million people.
Widodo was quick to visit the badly hit city of Palu, 1,500 km (930 miles) northeast of Jakarta less than two days after the quake, urging residents to be patient.
He made another visit on Wednesday, underlining the urgency of the rescue effort, as frustration about a lack of food, fuel and equipment mounted.
"Any failure to handle it properly is not going to go down well," Keith Loveard a senior analyst with advisory and risk firm Concord Consulting, told Reuters, speaking before Widodo made his second visit.
"It's still got to be managed and the next few days will be critical."
The government has left itself open to criticism for failing to maintain a tsunami warning system set up after a 2004 quake and tsunami killed 226,000 people in 13 countries around the Indian Ocean, including more than 120,000 in Indonesia.
The system has been out of action since 2012. Widodo, who came to power in 2014, said on Tuesday it had to be repaired and properly maintained.
With growing desperation and outbreaks of looting among survivors and questions over the aid effort, opposition politicians have been sharpening their knives.
An announcement by the interior minister, Tjahjo Kumolo, that survivors could take essentials from shops and the government would later compensate them, has been criticised as giving a green light to lawlessness.
"In a complex emergency, what is needed is leadership and law and order. At this stage, the government is very weak," Fadli Zon, deputy speaker of parliament from the opposition nationalist Gerindra party, said on Twitter.
Widodo's main challenger next year, Prabowo Subianto, is head of the Gerindra party.
'TARGET'
Widodo narrowly defeated Subianto in the last election in 2014 and Subianto will be looking for any opportunity to damage Widodo now.
"If Widodo pulls off a really good emergency relief effort he won't give Prabowo a target to strike," said Achmad Sukarsono of the Control Risks consultancy.
"At the moment, we haven't seen that so it's fair game for a challenger to attack."
Widodo also has to tip-toe around sensitivities over the issue of foreign aid in a country with a proud history of resistance to colonial rule, where governments have been loath to go cap in hand to outsiders.
Widodo risks angering either nationalists, by being seen as too ready to take outside help, or many ordinary members of the public, by hesitating to accept aid that could save lives.
Given the urgency in Sulawesi, even government critics begrudgingly agree outside help is needed, although one, Sodik Mudjahid, another senior member of Gerindra, added a word of warning:
"We should not commit to anything that will hurt our sovereignty," Mudjahid told Reuters.
Complicating the job for the government is a long history of bloodshed in Sulawesi between Muslims, who are a majority in Indonesia, and Christians.
An estimated 2,000 people were killed in three years of clashes in the region before a peace accord took effect in 2001. Palu was hit by bombings in 2005, believed to have been part of a campaign to re-ignite tension.
In the longer term, anger among people who feel deprived of aid could be manipulated.
"You've got a very polarised community," Loveard said.