RNZ reports the opposition leader Ishmael Kalsakau and Ephraim Kalsakau have quit, with other opposition members expected to follow.
The opposition leader said the amendment to the constitution should be done meticulously and there should be no political motivation.
Mr Kalsakau said he believes the people should be allowed to speak first before proceeding to parliament and in his view the bills were not debated in the interest of the people of Vanuatu.
The proposed amendments include regulating motions of no-confidence, by providing grace periods for when they may be filed.
This week's attempt to hold a no confidence vote failed with the government having the backing of 33 of the 52 MPs.