Kitui Senator Enoch Wambua now wants Kenyans to reject calls for a referendum.
Wambua who had earlier supported the proposals to amend the 2010 Constitution now says it is not a priority.
The senator elected on a Wiper party ticket claims that the push for constitutional change across the political divide is not genuine.
He argues that some politicians with selfish and personal interests want to create jobs for themselves at the expense of Kenyans.
Addressing the press in Kitui Town on Friday, Wambua said the majority of Kenyans do not want a referendum.
He stated that Kenyans are over-taxed and creating more job positions for politicians will be a burden to them.
Wambua added that a referendum will cost taxpayers Sh3 Billion, money he said can be channeled to development.
"We must ask ourselves hard questions and have this discussion soberly before agreeing to the referendum issue," Wambua said.
The debate on referendum continues to rage on as the majority of politicians push for it across the political divide.
Opposition leader Raila Odinga and his Wiper counterpart Kalonzo Musyoka are among the politicians advocating for the referendum.
Some of the politicians are pushing for a parliamentary system of governance.
Raila has been quoted saying that the bid for a referendum is unstoppable.