Prime Minister Prayuth Chan-ocha, a former army chief who led the 2014 coup, has publicly said he does not want to hold on to power and that the military is working toward restoring democracy quickly.
Getting a new constitution approved in a referendum is a key part of the junta's "roadmap to democracy" and a 2017 general election. It's also one of the biggest hurdles for the junta, known as the National Council of Peace and Order, because if the draft doesn't pass, it would add to pressure at home and abroad for a quick return to elections.
The interim constitution does not say what will happen if the draft is voted down, leading to more uncertainty.
"I don't know what is going to happen if the charter does not pass," said Meechai.
The constitution would be Thailand's 20th in 84 years of often turbulent democracy.
"Continuous making and remaking of constitutions takes up a lot of political energy, can cause instability and does not allow political arrangements to settle," said Sumit Bisarya, Constitution Building Head of Mission at International IDEA.
For the past decade, Thailand has been locked in a bitter conflict between the Bangkok-based royalist-military establishment and supporters of former Prime Minister Thaksin Shinawatra and his sister, former Prime Minister Yingluck Shinawatra, and their Puea Thai Party.
Meechai said the current draft, running at 261 pages, was not aimed at limiting the influence of the Shinawatra family, which has won every election since 2001, nor that of any political party.
"If people want to vote for Puea Thai, then they will get the vote," he said. "This charter is not designed to be an obstacle to any political party."
The referendum on the draft constitution is expected in July.