Parliament has so far been able to pass only six sections of the 13-section bill seeking to change the charter's provisions regarding the composition of the Senate.
This week will be the first time there will be five consecutive days of joint session, starting today. The debate will only focus on the make-up of the Senate.
Democrat MP for Nakhon Si Thammarat Apichart Sakdiset speculated that this week's session will be plagued with turbulence.
He said Pheu Thai will try to use the tactic of closing the session when Democrat MPs and senators debate the bill.
He was referring to a decision by Senate Speaker Nikom Wairatpanich to abruptly close the session on Wednesday last week after only seven of the 107 Democrat lawmakers listed to speak had debated Section 5 of the bill.
Mr Nikom's move prompted the opposition to petition the Senate on Friday, seeking the impeachment of its speaker for denying Democrat MPs the chance to debate.
Mr Apichart said his party deems the tactic as unconstitutional as lawmakers who had reserved the right to debate proposed changes must be allowed to do so. He said the Democrat Party still had two measures up its sleeve to block the bill and prevent its enforcement.
The opposition may lodge a complaint with the Constitution Court, asking it to issue an injunction to halt deliberations.
Once the amended bill is pushed through its third reading, it would not be enforced immediately as the court would need to consider whether the changes are constitutional.
The Democrats believe several changes breach the charter, he said.
A Democrat MP, who asked not to be named, stressed the opposition party will try to keep the debate going for as long as possible.
"Pheu Thai will not be able to achieve all its goals, including the 2-trillion-baht [infrastructure] loan and [the amended bill on] the composition of the Senate, within the next two years," the MP said.
Discussing this week's five-day session, Democrat MP Ong-art Klampaibul said the government whip should reschedule the meeting as lawmakers need to discuss issues of public concern on Wednesday and Thursday as usual.
The government is attaching more importance to charter amendment than the problems of the people, he said.
Meanwhile, Pheu Thai has stepped up pressure on its MPs and senators to show up for the parliamentary session.
The move came after Saturday's sitting was adjourned as a quorum was not met. Pheu Thai spokesman Prompong Nopparit said Sunday 26 lawmakers who were absent from the session must report to the party's senior figures to provide their explanations.
This will be their first warning, Mr Prompong said, but added that if they had failed to attend the session for trivial reasons, they will be punished.
Punishments include not choosing them to contest future elections, and if they are a government whip, removing them from the position, he said.
The failure to meet a quorum on Saturday was reported to have enraged Yaowapa Wongsawat, a senior figure in Pheu Thai.
She demanded talks with the missing lawmakers, according to a party source.
Pheu Thai list-MP Chinnawat Haboonpad, one of the MPs absent on Saturday, said many lawmakers had only been informed on Friday night about the session, and they had already returned to their constituencies.
Many had fixed their work schedules in their constituencies and could not change them, Mr Chinnawat said. He called for them to be treated fairly.
Prime Minister Yingluck Shinawatra stressed that lawmakers must perform their duties.
Some may have travelled to their constituencies, while others were tired after the long sessions in parliament, so it was important to seek ways to make the sessions closer together and adhere to meeting regulations, she said.
Noppadon Pattama, legal adviser to ousted prime minister Thaksin Shinawatra and a Pheu Thai strategic committee member, said absent MPs and senators must be held responsible for the lack of a quorum. A party meeting is expected to warn them, he said.
Pheu Thai cannot afford to be too complacent about the issue as the Democrats will try all means available to use delaying tactics, he said.