Some Jubilee Party leaders believe the Building Bridges Initiative (BBI) will be the final straw in the "sour" relationship between President Uhuru Kenyatta and his deputy William Ruto.
The Jubilee leaders, who feel the DP and his lieutenants have been undermining the Head of State through anti-BBI remarks, said Mr Kenyatta would rather cut links with Dr Ruto and back the task force that has brought peace to Kenya.
Nyeri Town MP Ngunjiri Wambugu and his Gatanga counterpart Nduati Ngugi criticised Dr Ruto and his allies for dismissing the 12-member task force.
On August 10, the DP tweeted: "The Jubilee administration will not be distracted from delivering on our manifesto and HE's Big Four plan by those engaged in the raging debate on Punguza Mizigo, BBI or 2022. They should be objective, truthful, and conduct an honest conversation that is in the best interest of all of us."
But Mr Wambugu told the Nation that Dr Ruto cannot purport to speak on behalf of the Jubilee administration, which endorsed the BBI to collect views on behalf of Kenyans.
Mr Nduati criticised the DP and his supporters, saying their failure to support the "handshake" meant they were opposed to the President's ideals and thoughts.