Communities Secretary Carl Sargeant said last month he was not convinced Communities First was the "most effective way to deliver for Wales".
He said there would be a new approach but, so far, community groups supported by the scheme say they are in the dark.
The Welsh Government said no final decision had been made.
In Swansea, Faith in Families, which runs three family centres, said it would be forced to close without Welsh Government support.
It is converting St Teilo's Church in Swansea into a Â£1m community hub with half the money provided by the Welsh Government.
Boss Cherrie Bija said: "We are not going to give up on these families."
She added that people were "really disappointed" after hearing the phasing out of Communities First would have a knock-on effect on the services the centre could deliver.
Communities First spends about Â£30m each year, with more than Â£300m spent since it was launched in 2001 and, at one point, it was supporting about 200 projects.
In Flintshire, Dave Wisinger, the county councillor for Queensferry, said the Communities First office covering his area provided crucial support.
"There has to be something else to take over," he said.
"And I would have thought the minister, if he has a serious look at this, he will appreciate the good work that's been done and he will keep these staff on, or as many as they can...maybe under another project."
Communities First supports four dementia cafes in Flintshire, helping those with the condition and their families, as well as running food banks, lunch clubs and family learning sessions.
It also runs job search clubs and employability courses.
Mother-of-two Kelly Latham from Garden City, who attended once such course in Mold, said: "I've been unemployed for nearly five years now.... child care's a big issue for me... and they've sorted it all out for me."
A Welsh Government spokesman said: "Although the communities secretary has said he is minded to phase out Communities First, no final decision has been made.
"We are currently seeking views on this and how to engage, support and strengthen communities and would urge anybody with an interest to have their say.
"It is too early to speculate on how any new approach might impact on particular areas."
Community groups are seeking assurances following the announcement that a scheme which supports deprived areas in Wales is set to be dropped.