Church leaders have also asked President Uhuru Kenyatta not to assent to the amendments.
Amani National Congress leader Musalia Mudavadi has urged the Senate to veto the controversial electoral law passed by the National Assembly last week.
At the same time, community leaders and traders in Nairobi on Tuesday vowed to counter planned Cord protests on January 4.
The Senate is on Wednesday scheduled to debate the amendments that have created anxiety after the Opposition threatened to call countrywide “mass action”.
Speaking in Sabatia, Vihiga County, on Tuesday, Mr Mudavadi called on the Senate to push for the formation of a mediation committee by turning down the amendments, approved in a chaotic National Assembly just before the Christmas break.
Senate Speaker Ekwee Ethuro has called a special sitting a week after the session that opposition MPs walked out of, claiming they were part of a plot to rig the election.
“We want victory through a fair and transparent election. What happened in Parliament is a recipe for a flawed election,” said Mr Mudavadi.
“All eyes are now on the Senate and we urge it to throw out the controversial amendments to allow the formation of a mediation committee,” he said.
This way, he said, the Senate would have offered the best gift to Kenyans.
The Amani leader asked why laws that were enacted through a negotiated agreement between Cord and Jubilee were being amended by “one side”.
In Nairobi, the Gikuyu, Embu and Meru Association (Gema) said it would not allow Cord to destroy property in the city, a stance echoed by Starehe MP Maina Kamanda.
“We will not allow loss and destruction of property,” said Mr Kamanda.
He accused Cord of using the contested amendments to gain political mileage.
“Cord knows that these amendments are necessary. They know that there is no full network in Kenya,” said the MP.
Gema Nairobi chairman Wilfred Kamau said: “We have lost a lot of property and even lives. So on January 4, we will mobilise our people to protect their interests.”
And in Makueni, Senator Mutula Kilonzo Jr said there would be no chaos in the Senate on Wednesday.
“There will be no monkey business or histrionics like those seen in the National Assembly,” he said.
Unlike the MPs, he said, the Senate Legal and Human Rights Committee chaired by Busia Senator Amos Wako would collect public and stakeholder views on the laws before the debate goes to the floor.
“Members of the press are invited to the sessions,” he said.
Additional reporting by Pius Maundu.