Mukherjee, along with Parliamentary Affairs Minister PK Bansal and Human Resources Development Minister Kapil Sibal, held meetings with BSP leader Satish C Mishra and RJD chief Lalu Prasad as the debate was underway in the Rajya Sabha.
The BSP has 18 members and the RJD four in the 243-member House.
Sources said Mishra and Prasad were asked about the stand of their parties on the Lokpal Bill and how they would vote.
Mishra told Mukherjee that the BSP was opposed to the Lokayukta provision as it goes against the sprit of federalism.
The government side told him that it would get back, the sources said.
The BSP remained firm on its opposition to the clauses on Lokayukta although it has not moved any amendment. There were also indications that BSP members would not walk out during the vote.
Meanwhile, in indications of further problems for the government, two Congress members, P Kannan and Vijay Darda, were not present in the House during the debate. Congress has 71 members, altogether.