More than 120 Labour MPs were poised to vote against the Universal Credit and Personal Independence Payment (PIP) Bill on Tuesday.
The changes come after a ring-around by cabinet ministers failed to bring rebels on side.
The bill was intended to restrict eligibility for the PIP – the main disability payment in England- and limit the sickness-related element of universal credit, to help shave £5bn off the welfare budget by 2030.
Sky News political editor Beth Rigby has heard that existing PIP claimants will be able to keep their payments, which means 370,000 people will not lose out. This will cost the government at least £1.5bn, according to the Institute for Fiscal Studies.
Sky News understands that a senior source has accepted the change, but it will be up to each individual rebel to make a decision on whether to withdraw.
The source said they think the changes are a “good package” with “generous concessions”.
Politics latest: Government to make offer to rebels
A reasoned amendment signed by 126 Labour MPs argued that disabled people had not been properly consulted and further scrutiny of the changes is needed. If passed, this would have killed the bill.
Other concessions offered by the government include allowing existing claimants to keep the health element of Universal Credit.
Sky News understands that some senior rebels are willing to accept the concessions – with one saying that “the concessions will be positively received, and I expect to vote with the government now”.
Other MPs who had not wanted to rebel were also expecting to change their votes.
However, several Labour MPs on the left of the party have gone public to say they will still oppose the government, including Diane Abbott, Richard Burgon, Nadia Whittome and Brian Leishman.
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