Re-assessments of severely disabled people unhappy with their care packages will not begin before July.
The Welsh Independent Living Grant has ended with councils funding care for more than 1,000 people receiving it.
In February, the Welsh Government announced anyone unhappy with their new council care package would be offered independent re-assessments.
Plaid Cymru said the wait was “way too long”. The Welsh Government has been asked to respond to the criticism.
In response to a Freedom of Information request, the Welsh Government told BBC Wales it has set aside up to £60,000 to pay an independent organisation to do the reassessments.
It anticipates the contract will be awarded by the end of June and re-assessments will begin in July.
£2.4m per year has also been budgeted, “for planning purposes”, to cover the potential costs of any increased packages.
157 people out of 1,174 assessed by their councils by the end of last year had had their support reduced.
There have been big regional variations, with cuts most common in Wrexham, Newport and Ceredigion.
The WILG was introduced in Wales to replace the UK-wide Independent Living Fund (ILF), which was closed down by the UK government in 2015.
In a letter to ex-WILG recipients, Deputy Minister for Social Services Julie Morgan said their “patience” would be appreciated.
“I do not want people to be waiting for an independent assessment,” she said.
“However, it is important to organise these independent assessments properly, so that they meet the required standards.”
Plaid Cymru’s social justice spokeswoman Leanne Wood questioned whether the reassessments were necessary.
“Initially many of these people were given an award for life and going through a reassessment process is extremely stressful,” she said.
“Particularly if you have a condition that everybody knows is not going to improve, it’s only going to deteriorate.
“So putting people through those reassessments is potentially problematic but at the same time this does need to be resolved quickly.”
Nathan Davies, a Labour member and founder of the Save WILG campaign, said the wait was “inconvenient” but criticised the previous Welsh Labour Government, led by Carwyn Jones, which made the initial decision to transfer the responsibility to councils.
“The fact that they [the current Welsh Government] are having to do this work now is because the previous neo-liberal regime did not listen to our campaign team and disregarded the evidence that we presented.
“The fact that we are having to endure an uncomfortable few months is totally down to them and a number of irresponsible local authorities.”
You can see more on this story on the BBC Wales Live programme at 22:30 BST on Wednesday BBC One Wales, and then on BBC iPlayer