Members of both the SNP and Labour backed the joint approach, which was floated in an article in The Scotsman by Edinburgh city council leader Andrew Burns yesterday.
Mr Burns, who heads a Labour-SNP coalition, urged Alex Salmond and Johann Lamont to back an alliance similar to that agreed between the two parties in the capital.
Last night, there were calls from both side for an anti-Tory alliance to oppose coalition policies such as the “bedroom tax”.
Holyrood’s welfare reform committee convener Michael McMahon, a Labour MSP, said he would bring forward a proposal to the parliament demanding a deal on formal co-operation between the two parties.
Mr Burns had said a new consensus on the bedroom tax –which imposes a levy on welfare claimants living in under-occupied homes – and other issues could help politicians at Holyrood to win back the “trust and respect of the electorate”.
Former Holyrood Labour minister Malcolm Chisholm said the contribution was “very significant” and backed co-operation on key issues between the two parties.
Mr Chisholm, MSP for Edinburgh Northern and Leith, said: “We ought to work together”.
SNP MSP Jamie Hepburn said the call from Mr Burns was “broadly speaking correct”. He added: “Where we can work together, we should do that. I’d work with anyone to stop the worst effects of these changes.
“There’s been a strong lead from the Scottish Government, and it should be possible to work together.”
Former Labour first minister Henry McLeish said it was a “worthy call” from Mr Burns.
He said: “A united front is needed in Scotland when there is really bad legislation from Westminster. We need to support Scotland and people who would be damaged by these policies.
“There’s no reason why Labour and the SNP shouldn’t get around the table and put down a marker to say enough is enough from Westminster.”
Mr McLeish said Holyrood needed “a new narrative” along similar lines to the pact agreed between Mr Burns and his SNP deputy leader on Edinburgh council, Steve Cardownie.
Meanwhile, Mr McMahon said he “totally agreed” with Mr Burns and would ask Holyrood’s welfare reform committee to request an alliance between Mr Salmond and Ms Lamont.
Mr McMahon said: “Everyone has got to get around the table and talk about how we can come up with something, as the approach is too piecemeal at the moment on opposing this.
“The constitution is not important on this issue, but the people who are adversely affected by welfare reforms are.
“We have to agree how we can use the devolved powers we have to oppose the UK government over its welfare policies.”
Council leader Mr Burns said the response to his call “bodes well” .
He added: “I’ve been pleasantly surprised by the level of constructive feedback, but I’m not naive enough to think it could impact on the constitutional debate.
“There are whole swathes of domestic issues we agree on. If we can do it in the Edinburgh council chamber, I’d hope that in the Holyrood chamber there could be some debate on this.
“It bodes well for domestic issues, and I’d hope it will make people pause for thought at Holyrood.”
Other MSPs from Labour and the SNP backed the calls, but voiced criticism of their opponents and the way they had opposed the welfare shake-up.
Labour MSP Elaine Smith said the SNP government should “take a lead” and provide funds to councils to stop evictions of tenants affected by the bedroom tax.
SNP MSP John Mason said both parties “could agree on more than we do”, but blamed Labour for lack of co-operation.