The 194-page draft of the charter is supposed to pave the way for elections promised in 2010 in which the country's military leaders will retain key powers in a "discipline-flourishing democracy".
But Aung Din, director of the US-based advocacy group US Campaign for Burma, told The Associated Press on Monday that "nobody is interested in going to vote".
"People are trying to rebuild their lives, find their families and friends," he said.
"Soldiers are used to arresting democracy advocates, but now they're
nowhere to be seen," he said.
Myanmar's opposition National League for Democracy (NLD) party says it is "absolutely inappropriate" for the government to persist with the constitution amid the post-cyclone devastation.
"They should show their goodwill toward the people by co-operating with the international community, but we have seen no sign of that goodwill," said Nyan Win, an NLD spokesman.
The party, led by detained Nobel laureate Aung San Suu Kyi, is campaigning for a "no" vote in the referendum.
But public opinion, and whether or not voters in cyclone-hit areas can physically reach polling stations, does not appear to be the government's concern, according to political analysts.
"The military regime has never had any intention of holding a free and fair vote," Monique Skidmore, a Myanmar expert and professor at the Australian National University, said.
"They don't care if everyone votes or not. They care about the outcome and I have no doubt they will manipulate the outcome in their favour."
The government declared five states - with a total population of 24 million people - disaster zones after Cyclone Nargis tore through the Irrawaddy delta on Saturday before hitting Yangon.
Thailand-based Myanmar analyst Aung Naing Oo said the government could use the cyclone to manipulate the vote and delay the announcement of the result.
"They're immune to criticism and they're so proud. They won't ask for foreign help and risk compromising the referendum. It's their baby and they're ready to go ahead with it," he said.
Myanmar, formerly known as Burma, has been under military rule since 1962.
The military refused to honour the last election in 1990, in which the NLD won a landslide victory.