Many families have already evacuated to safer places and the rest are preparing to move at short notice in case the dike falls through.
"If the embankment gives in the entire area would turn into a massive pool within minutes with huge waters rolling," one resident said.
Bangladesh's Prime Minister Sheikh Hasina visited the embankment yesterday and called for a vigil. "Allah often tests our faith by putting us in danger," she said. "So be patient and confident as you struggle to save the dike."
The 10-mile embankment also serves as a highway linking Dhaka to the towns of Demra and Narayanganj.
The emergency operation was stepped up as monitors reported that the flooding, which has already killed at least 823 people across the country, showed no sign of letting up.
All the country's major rivers, including the Padma, Brahmaputra and Meghna, rose at different points yesterday, inundating fresh areas and aggravating conditions elsewhere.
The floods, triggered by rain and fed by water rolling down from India, have ravaged the country for more than two months, leaving some 25 million people homeless or stranded.
Bangladesh is a country of disasters. The only popular reference to Bangladesh that springs to most people's minds is probably the George Harrison album, prompted by a famine.
If it is not demonic cyclones or overturning ferries, it is floods or arsenic in the wells.
In Dhaka, the transnational disaster managers - the United Nations, the World Bank, Oxfam, Care and the rest - are a permanent presence, their four-wheel drives towering above the autorickshaws.
But with its present floods, Bangladesh has outdone itself. Yesterday, Michael Elmquist, head of a United Nations disaster assessment and co- ordination team, said: "The unfolding situation is the most serious the country has ever faced."
After a slow start, relief has begun to arrive: the UN's World Food Programme expects to deliver food worth $76m (pounds 46m) in what it describes as "the biggest emergency in the Food Programme's history".
Relief agencies will also have to deal with a shortage of drinking water. Most of the nation's 120 million people depend on wells for drinking water. But tens of thousands of wells across Bangladesh are now submerged.Reuse content