Both the Democrat and Pheu Thai parties are concerned that clauses in the draft charter put their stability at risk.
They have criticised provisions on the electoral system and political parties in particular.
Flaws in the draft charter were highlighted ahead of a Charter Drafting Committee (CDC) forum today in which political parties are likely to air their grievances on the provisional constitution.
Samart Kaewmeechai, a former Pheu Thai MP for Chiang Rai, raised several issues after studying the outlines of the draft charter.
Mr Sumart will attend today's forum along with Pheu Thai acting deputy secretary-general Chawalit Wichayasuth.
Clauses that refer to elections in the draft charter will ruin the political party system because they will weaken parties and force them to fade out, Mr Samart said.
Political parties will dissolve because most, if not all, election candidates will opt for independent candidacy, he predicted. As independent candidates they won't have to declare their policies, he said.
Mr Samart said he believed the new election system would make vote buying a bigger problem.
Unlike independent candidates, those who represent political parties at elections will have to define the sources of the funds they will use to implement their policies if they win enough seats to form a government, he said.
Former deputy Democrat Party leader Jurin Laksanavisit echoed Mr Samart's point of view.
He said the CDC had tried to undermine political parties by exempting election candidates from having to apply for membership of a political party to qualify to run in a general election.
Candidates will be required to undergo an assets check by a new committee when they apply to run in elections, Mr Samart said.
If the assets examination committee is not politically neutral, problems could result, as they could attempt to stop opposition candidates running in elections.
Government stability is also at risk from the proposed electoral system, not only because it will consist of independent MPs, but because the prime minister won't have to be installed at an election, Mr Samart said.
He disagreed with the proposed increase in the power of the Senate. The CDC wants a stronger Senate to keep the government's power in check. It is also proposing the Senate have the power to introduce its own bills without having to forward them to the lower House for scrutiny. This will reverse the order of the legislative procedure, he said.
Mr Samart also opposed a proposal in the draft charter in which a people's assembly will hold local administration bodies' powers to account. The new checks-and-balance mechanism is a good idea, but if in practice it lacks transparency and fairness, it will end up becoming a new source of political unrest, he said.
Mr Jurin, meanwhile, opposed a proposal to dissolve parliament in the case of a prime minister's impeachment, saying it would not be fair to punish MPs for someone else's mistake.
Also problematic would be a CDC proposal to require the votes of half of parliament (both MPs and senators) to endorse the impeachment of a prime minister, instead of the two-thirds of the Senate currently required, he said.
He also objected to a proposal to shift the duty of organising elections from the Election Commission to the Interior Ministry, saying Thailand recently experienced a crisis due to the ministry's mismanagement of polls and should not risk this happening again.