Deputy President William Ruto's comment on the proposed referendum has rattled Western leaders who are for the idea.
While in Sirisia on Sunday, the DP termed plans to amend the Constitution as a daytime dream.
He said for "individuals who ought to retire from politics honourably".
The comments saw Ford Kenya leader Moses Wetang'ula, Cotu secretary general Francis Atwoli and MPs tell off Ruto.
Senator Cleophas Malala, Nominated MP Godfrey Osotsi, and Busia Woman Representative Florence Mutua held the first presser on the matter.
Shortly after them, Atwoli came out saying Ruto should "contemplate resigning if he is against the proposed referendum."
In his statement, the Cotu boss was categorical that a review of the 2010 Constitution is a must.
"We must do it to address the winner-takes-it -all governance arrangement in the country," the unionist said.
He asked Ruto to borrow a leaf from the late Jaramogi Oginga Odinga who resigned from government in principle after disagreeing with President Jomo Kenyatta.
"We must have a relook at our laws on power structure to help contain the various ethnic interests in the country," Atwoli said.
"It is no longer tenable to have violence and chaos after every election. We must see how to accommodate every shade of interests in our country."
"Whatever I have proposed comes to pass. We will go next elections in 2022 under a new supreme law of the land," he added.
Atwoli faulted the DP on his choice of words at the weekend during a campaign stop in Western Kenya.
The DP was quoted as dismissing the referendum call as being pushed by "foolish idlers who ought to retire."
"He cannot claim that those supporting the call to review the constitution including the President are foolish," Atwoli told the deputy president.
The COTU boss also dismissed the DP's "numerous trips" saying they won't yield him much support.
"The numerous trips he makes across the country, especially in Western will not help him. There are no votes in the markets in western that he frequents," Atwoli said.
Wetang'ula held his presser at his Kanduyi home. He was accompanied by
He said Kenyans voted for the Constitution "with the right to determine the fate of the same, including its change."
The Bungoma Senator told journalists that the country must go back to a parliamentary system or a mixed system.
He describe the current government as "restrictive" and one which cannot be banked on to unite the country.
Wetang'ula warned Ruto saying he risks being "consumed by the force of the good idea that has come."
"When a good idea comes, those who are resisting it must learn from history that they stand a risk of being consumed by its force."
The lawmaker said that with like-minded leaders, he will champion for a referendum "not because we (proponents) want accommodate a few individuals."
He said those who could be salivating for positions in the changed draft that have no guarantee that they will get it.
"There are people who pushed hard for the current Constitution thinking they will benefit from it with positions but to date they haven't," Wetang'ula said.