The peak body for social services has called for Labor to back out of a deal with the government to pass harsh welfare measures on skilled migrants.

It’s feared the bill, expected to pass next week, will lead to an increase in the number of people seeking emergency relief from charities and community groups, and a rise in child poverty.

Labor said it had agreed to support the Coalition’s bill – touted to bring $1.3bn in savings – in exchange for amendments, rather than see it passed with the support of One Nation in its original, harsher, form.

However, on Thursday, it became apparent that enough crossbenchers had been against the bill that it could probably have been defeated with Labor and the Greens.

“We’re really hoping that Labor changes its mind over the weekend, but if it does go through it will see certain groups of people have to wait for up to four years to access payment,” said Charmaine Crowe, social security policy officer for the Australian Council of Social Services (Acoss).

“Our concern is that this is going to lead to an increase in child poverty in Australia, which is trending upwards anyway, and we’ll have this absurd situation where two families in the same situation will be treated differently simply because one family recently arrived in Australia.”

The proposed amendment will force newly arrived migrants on skilled worker visas to wait longer for various social services, including four years for access to Newstart, Youth Allowance and Austudy, one year for parental leave and one year for Family Tax Benefit A. The Coalition had been seeking a blanket four-year wait.

“We know that when people can’t access support payments because of waiting periods, in many instances they’re on their own,” Crowe said.

“We’d expect this bill would lead to an increase in people having to access emergency relief because they’re left without support.”

Crowe said Acoss feared the new waiting times for Family Tax Benefit A would have the biggest impact.

“Now Labor is fully aware they would have the numbers in the Senate to block the worst parts of this bill, we’re calling on Labor to change its position and make sure the current waiting periods aren’t extended, and we don’t have them imposed on low-income families accessing FTB part A.”

The shadow treasurer, Chris Bowen defended the deal, saying Labor had “no truck” in having a blanket four-year waiting period, and it was “ill-advised” for anyone to think they could predict a vote in the Senate.

“We in all good conscience, thought about this very carefully, decided it was best to protect hundreds of thousands of people from the impacts, and we’ve done that,” he said.

“Greens and others can grandstand all they like but the Labor party protected hundreds of thousands of people.”

The revelation that the bill could be defeated prompted a turnaround in support from the Federation of Ethnic Communities’ Councils of Australia, which had given support to Labor’s compromise.

“This bill will inflict unnecessary hardship on vulnerable people and is due to be voted on in the Senate shortly,” said the Fecca chair, Mary Patetsos.

“Earlier this week Fecca accepted amendments to the bill on the understanding that there was not enough support in the Senate to defeat it. Fecca now believes that …there are sufficient crossbench senators prepared to vote against this legislation.”

During Senate debate on Thursday, several crossbenchers expressed fury at the Labor party for making the deal.

“It seems that the Labor party is more concerned about the money saved than the welfare of new arrivals in Australia,” said independent senator Tim Storer.

He said migrants made an “incredible contribution” to society and contributed to the growth and prosperity of the country.

“Why should they not also have access to the safety nets we have in place to support people when times are tough?” he asked.

The Greens senator Mehreen Faruqi said she and her husband had relied on support when they arrived in Australia as qualified engineers.

She said they were told there was a lot of demand for engineers and plenty of jobs in Australia when they arrived but the reality was very different.

Faruqi said the support system at the time recognised that new migrants needed financial assistance and it was “the only way we could have a roof over our head and food on the table”.

“As a migrant I find Labor’s position on this disgusting and cowardly,” she said.

“Don’t sit here and pretend you had no other option when it is your votes that will pass this bill.”

The Greens community services spokeswoman, Rachel Siewert, said Labor had not consulted with the crossbenchers.