Former prime minister Manmohan Singh and former finance minister P Chidambaram are not among the signatories to the impeachment motion notice against Chief Justice of India Dipak Misra.
The Congress, however, downplayed it saying the party did not want to involve its senior leaders in the issue.
The impeachment notice has been signed by 64 Rajya Sabha members from seven political parties, besides seven MPs who have since retired.
Congress leaders Ghulam Nabi Azad and Kapil Sibal rejected insinuations that there was a 'division' within the Congress over the issue and there was no consensus among the opposition parties.
Azad said there are parties which have signed and there are parties which have not and were not available, 'but all are supporting'.
On the issue whether consensus eluded the opposition parties on the issue, Sibal said 'there is consensus'.
To a question about reports that Manmohan Singh was reportedly opposed to the decision, Sibal that 'this is absolutely false. This is not true at all. From the very beginning, this is a very serious issue'.
"It is not instant coffee... The decision was required to be taken after serious and well-thought discussion.
"Since the issue dealt with the Constitution, we have deliberately not included Dr Manmohan Singh as he is a former prime minister. With regard to some others, whose cases are going on, we did not wish to embarrass them," Sibal told reporters.
The Congress leader said the impeachment motion is not to be moved by parties.
"So do not make this political. This is something that is in relation to the independence of an Institution and has no political motivation behind it," he said.
Among the signatories include 45 MPs of the Congress besides six former party MPs who have retired recently, including its senior leaders Azad, Sibal, Anand Sharma, Ahmed Patel, A K Antony, Motilal Vora, Ambika Soni, Jairam Ramesh and Abhishek Singhvi.
Among the other signatories to the impeachment notice are four MPs from the Nationalist Congress Party, including Sharad Pawar, Praful Patel, Majeed Memom, besides a retired MP D P Tripathi, eight MPs of Samajwadi Party including Ram Gopal Yadav and Neeraj Shekhar.
Besides, three MPs of Communist Party India-Marxist and one each of Bahujan Samaj Party (Satish Chandra Misra), Communist Party of India's D Raja, Indian Union Muslim League's P V Abdul Wahab and nominated member K T S Tulsi have also signed the petition.
Meanwhile, amid reports that there was division within the Congress over the move to impeach the CJI, senior Congress leader Salman Khurshid said impeachment is too serious a matter to be discussed publicly.
"Impeachment is too serious a matter to be played with on the grounds of disagreement with any judgement or with any point of view of the court.
"I am not a party to or privy to the discussions that have taken place between different parties. Therefore, for me to reflect specifically on whether the grounds are justified or not justified, would be unfair," he said on being asked whether he agreed with the decision.
He said whatever decision is taken by the party, it will present that decision before all and will give a clarification.
"This is a sensitive issue and I don't think this issues needs to be discussed publicly and put question marks on such places where question marks should not be put.
"The Supreme Court's decision is final and politics should be kept away from it," he said.
However, the Congress communications in-charge rejected all such insinuations that there was division within the party on this issue, saying all such reports are 'false'.