The Pheu Thai Party has not ruled out the possibility of amending the charter in time for the next election as long as certain compromises can be agreed upon.
Prime Minister's Office Minister Chousak Sirinil, who is also the party's chief legal expert, outlined three possible scenarios for passing a revised constitution.
These were that parliament waits 180 days to press on despite senators' disagreement over the referendum law, the differences being settled without delay, and amending the constitution without passing the law first.
The scenarios were being considered after Nikorn Chamnong, secretary of the joint House-Senate panel on the charter referendum bill, last week said he was becoming resigned to the likelihood the amendment may not be completed before the next general election in 2027.
Mr Nikorn was reacting after the Senate voted to insist on the double-majority rule being imposed on a referendum.
The rule -- that at least half of all eligible voters must cast their votes and that the winning outcome must be supported by at least half of the voters who turn up at polling booths -- was shot down in the House.
However, when the Senate was handed the referendum bill for deliberation, it reinstated the double majority requirement.
Most parties, including Pheu Thai and the main opposition People's Party, wanted the double majority rule dropped in favour of a simple majority to be applied in the referendum.
They argued that a double majority was too hard to achieve.
PP list-MP Parit Wacharasindhu said he was concerned a campaign may be launched to persuade voters to stay away or even boycott a referendum as part of a tactic to make the double majority fall short.
Critics, however, maintained there was no problem with the rule being enforced in the previous referendum in which the current constitution was passed.
After the Senate recommended reverting to the earlier rule, a joint MP-Senator panel was formed to thrash out the differences between the two Houses.
If they cannot reach an agreement, the referendum bill will be suspended for 180 days. After that, if the House stands its ground on the simple majority, it can enact the bill, said Mr Parit.
However, the delay has raised fears of a failure to hold a referendum within the current government's term which could push back charter change at least until after the next general election.
Mr Chousak on Saturday said Pheu Thai was aware of the hindrances ahead and party executives were trying to find a solution.
He also admitted the party was trying to figure out how to rewrite the charter without passing a referendum bill first.
Anusorn Iamsa-ard, Pheu Thai list MP, said finding a compromise among lawmakers was key to resolving sore points in the referendum bill and keeping the original charter amendment timeframe intact.