Senior Congress leaders on Monday also met Samajwadi Party chief Mulayam Singh Yadav for help as the Bharatiya Janata Party (BJP) was ready with its strategy for the budget session.
According to reports, Rashtriya Janata Dal (RJD) chief Lalu Prasad has played the role of mediator for Congress.
The Prime Minister has also invited all the UPA allies for dinner on Tuesday as the Congress heading the UPA may not be in a position to take even the allies for granted with a key coalition constituent Trinamool making it clear it was against a cut in fertiliser subsidy, NCTC and rise in petroleum prices.
Trinamool supremo Mamata Banerjee has joined non-Congress chief ministers in opposing the proposed National Counter Terrorism Centre(NCTC).
However, expressing confidence that the budget session of Parliament would run smoothly, the Prime Minister said the government was willing to discuss and debate all issues on the floor of the house.
"I think dealing with pressure is part of the parliamentary life. I am confident that we have all the numbers that are needed," Manmohan Singh told reporters ahead of the budget session starting from Monday.
He added that he was confident that the budget session would run smoothly.
"We are willing to discuss and debate all issues on the floor of the House. I appeal to all the political parties to work together and cooperate in meeting the challenges," he said.
Brushing aside speculation of a mid-term poll, the Prime Minister has also expressed confidence that the UPA government would complete its term as it had the needed numbers.
Bonhomie in Rajya Sabha on opening day session
The first day of the budget session of Parliament began on a warm note in Rajya Sabha with Prime Minister Manmohan Singh exchanging pleasantries with the Leader of the Opposition Arun Jaitley as well as members from other opposition parties and UPA allies.
As soon as Singh arrived in the House after the President's Address to the joint sitting of Parliament, leaders from various parties greeted him.
Apart from Jaitley, BJP leaders SS Ahluwalia and Balbir Punj, JD-U members Shivanand Tewari and NK Singh walked up to the Prime Minister to shake hands with him. The Prime Minister also waved at Opposition members.
Defence minister AK Antony walked up to the Opposition benches and chatted with leaders of BJP, Left, SP and BSP.
The Prime Minister was also seen interacting with CPI leader D Raja minutes before the House was called to order.
(With inputs from PTI, IANS)