Social Development Minister Mervyn Storey will bring the Welfare Reform Bill back to the assembly next Tuesday, along with a new implementation plan.
Sinn Féin wants other parties to back a petition of concern against the bill.
Talks between the parties and secretary of state on Wednesday failed to find a resolution to the crisis.
On Thursday, SDLP leader Alasdair McDonnell said his party was hopeful progress could be made on getting an independent economic think-tank that would help with what he called "a total re-engineering of our economic strategy".
He added that recent engagement with the other parties had been "very positive" and some of their concerns "were being listened to".
Mr McDonnell said there were "96 hours before next Tuesday" and they would be meeting on Thursday, Friday and over the weekend, both internally and with other parties.
"The engagement with other parties has been very positive on many aspects of this arrangement," he said.
"We had very useful discussions yesterday with some of the other parties and the people in DSD [the Department for Social Development] and a lot of our issues, it would appear, can be factored into a solution.
"Our job is to protect those in the margins of society and we're going to do that and we're relieved that at least we're being listened to now, whereas we were being dismissed out of hand by others who then have changed their minds."
Mr McDonnell described it as "a very fluid situation."
His party colleague, Fearghal McKinney, said they put before the secretary of state an economic agenda that shifted the context of welfare reform.
"Where was it ever ordained that we should be so heavily reliant on welfare?" he said.
"We need a different game-changing discussion that puts ambition at the heart of our politics."
The Northern Ireland parties had agreed a deal on Westminster's welfare reform in the Stormont House Agreement last December.
However, Sinn Féin withdrew its support for the bill in March.
The DUP has warned that if Tuseday's bill is not passed the assembly could collapse.
The SDLP has refused to say if it will back a Sinn Féin petition to block the welfare reform bill if its brought to the floor of the assembly next week.