Leighton Andrews' controversial Local Government Bill was pulled from the Assembly agenda today where a final vote was due to take place on it.
Opposition members have all spoken against the Bill which paves the way for Council mergers and without support from at least one opposition member then Labour do not have enough votes for it to pass.
Mr Andrews is the Minister for Public Services and is also the current AM for the Rhondda.
Karen Roberts, Welsh Liberal Democrat Assembly candidate for the Rhondda said
"As we have said previously we are in full agreement that there needs to be a cut in the number of Councils in Wales. However, the way in which this has been handled by the Minister all along has been nothing short of arrogant.
"He has come up with an arbitrary map which sees, for instance, Rhondda Cynon Taff lumped in with Merthyr and Bridgend to form a very large Local Authority which will take democracy further away from residents.
"Many in his own party disagree with the way he has tried to steamroller these proposals through.
"A spokesperson said that the vote had been postponed to allow for further cross party talks to try and reach a consensus.
"The Welsh Liberal Democrats at the Assembly have made it clear they would not consider voting for this unless it contained a commitment to a fairer voting system.
"Until now the Conservatives and Plaid have also been against it. It will be interesting to see whether they hold that line."