Nyan Win, spokesman for her National League for Democracy, said an effective army veto in parliament meant the NLD could not prevail in its efforts to overhaul the constitution during an ongoing debate in parliament.
Parliamentary representatives of the powerful military have lined up during the debate to voice opposition to any change that would threaten their position in the legislature, where they hold a quarter of all seats.
"So why are we working for it? Because we believe in democracy," he added, in some of the party's most downbeat remarks on a charter which many believe was specifically designed to thwart Suu Kyi's political rise.
Legislators will choose a new president after a general election in November 2015, which Suu Kyi's party is expected to win if polls are free and fair.
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US President Barack Obama last week raised concerns about the clause, saying "the amendment process needs to reflect inclusion rather than exclusion".
Parliament speaker Shwe Mann said Tuesday a referendum would be held next May on any charter amendments approved by parliament after the current heated debate in the capital Naypyidaw.
The Speaker said it would be impossible to implement any major constitutional changes until after next year's election, which is seen as a test of the country's transition that began in 2011 from outright military rule.
At party headquarters in Yangon a handful of activists sold Suu Kyi T-shirts and trinkets as the routine continued as normal.
But Myanmar-language newspapers sounded the alarm today.
"Parliament will approve the constitutional amendments only after 2015: Daw (honorific) Aung San Suu Kyi cannot be president," said Mizzima in a front-page commentary.