A section of leaders has accused those opposed to the Building Bridges Initiative (BBI) of plotting to scuttle the quest for a united nation.
Led by nominated MP Maina Kamanda, the leaders said the quest for a referendum is not a question of if but when.
They asked those supporting Thirdway Alliance party leader Ekuru Aukot's Punguza Migizo initiative to rethink their stance.
Mr Kamanda praised the BBI as people-driven process.
"There is no turning back, the referendum should come faster so that we amend the Constitution. We are fully behind President Uhuru Kenyatta and the ODM leader Raila Odinga," said Mr Kamanda.
He was speaking during a church service at Oljororok Catholic Church in Nyahururu on Sunday where he was accompanied by a host of Jubilee Party politicians allied to team Kieleweke.
The nominated MP said the referendum will lead to a more united country and also make it hard to be corrupt to go scot free.
"You have seen how governors are stealing public money in the counties, theft is also in the national government. This is what we want to stop. We want to make it hard for them to steal public funds.
"We also want to cement the unity handshake has brought by ensuring that all communities are equal," he added.
He hit out at politicians in the Tanga Tanga wing to stop their constant attack on Mr Odinga.
"Is he not Kenyan? Mr Odinga's unity with President Kenyatta has brought unity to the country. We now want the handshake to go to mashinani, (grassroots), " said the lawmaker.
Former Dagoretti South MP Dennis Waweru said that the BBI team reached out to people from all walks of life to get their views in a people-driven process.
He questioned why proponents of Punguza Mizigo Bill were reluctant to give their views to the BBI team during its sittings across the country.
"Every person was given an opportunity to present his or her views to the task force and those behind Punguza Mizigo should have presented their views to the team," said Mr Waweru.
Mr Waweru said Kenya is ripe for a referendum.
"We were warned by religious leaders that some parts of the Constitution needed to be amended and we said we would do so later, that time has now come," he said.
He urged leaders to support President Kenyatta and Mr Odinga in uniting the country and delivering on Big Four Agenda.
The Kenya Investment Authority director castigated leaders who are fighting the President and handshake.
"We told the president that the first thing he had to do in his second term was to unite the country and that is what he is doing. We are supporting his fight against corruption," said Mr Waweru who dared those who do not support the process to resign.
Other leaders present also supported the calls for a referendum.