Nikorn Chamnong, a member of the joint House-Senate panel on the charter referendum bill, said on Wednesday he no longer expects the public vote to take place in February as planned.
Both chambers have set up a committee to resolve their differences regarding the size of the majority needed to pass a referendum on amending the charter.
The House stands by its position that a simple majority vote is sufficient for it to pass while the Senate insists on two conditions: over 50% of voters must participate in the referendum, and the majority of those who take part must support it.
Mr Nikorn said the joint committee has yet to schedule a meeting to discuss the matter and that even if they can reach a conclusion by Oct 28, there is not enough time for each chamber to endorse the resolution before Parliament's current session concludes on Oct 30.
He said the issue is not urgent enough to justify calling a special session next month (in November) and the joint committee is likely to wrap it up in the next session which starts in December.
"While the bill's deliberation could be completed and the law take effect, the charter referendum tentatively scheduled in early February cannot proceed as planned," he said.
The government plans to hold the referendum alongside nationwide local elections in February to save on costs, which are estimated to be between 2-3 billion baht.
Wisut Chainarun, a Pheu Thai MP and chief government whip, said if the committee cannot reach a conclusion, the referendum bill will be suspended for 180 days before being submitted for royal approval.
He declined to discuss possible solutions, saying the matter should be left to the joint committee.
Thai Pakdee Party chairman Warong Dechgitvigrom expressed concerns on Facebook about the switch to the simple majority.
He said even though political parties promised not to touch Chapters 1 and 2 of the charter in the event of a rewrite, the simple majority requirement would make it easier for future amendments to be passed.
Chapter 1 contains sections defining Thailand as a single, indivisible kingdom with a democratic regime and the King as the head of state. Chapter 2 stipulates sections on royal prerogatives.
He urged political parties not to fall for the argument for the simple majority requirement, saying it is also their job to defend a constitution designed to combat corruption.
The two requirements have been criticised for making it difficult for a referendum to achieve the minimum requirement.