Some senior Liberal Democrats say they would strongly oppose a new coalition with Labour in the Welsh assembly.
Welsh Labour leader Rhodri Morgan could ask the Lib Dems to share power after his party fell short of a majority.
But Lib Dem leaders of four Welsh councils say they are all against it, amid doubts raised over the assembly group leadership of Mike German.
As parties prepare for post-election talks AM Eleanor Burnham said Lib Dems had to listen to councillors' views.
Labour is due to meet next Tuesday, before the new assembly sits for the first time on Wednesday.
Mr Morgan said he would spend the time before then making "lots of phone calls" to fellow Labour AMs. A new assembly government has to be formed by 24 May.
Thursday's election left Labour with 26 seats in the 60-member assembly, down three on when the campaign began, and down four on the last election in 2003.
Although Lib Dems are the smallest major party, with six seats, they could prove crucial. They are regarded as the most likely Labour partners in the next assembly government, having already formed a coalition from 2000 to 2003.
After senior Lib Dems met in Cardiff on Saturday, they said they would "reflect further" on the election over the next few days.
"We will act responsibly," they said in a statement. "Stability is important to the next government of Wales."
It came after some party figures aired their concerns. Lib Dems run four local authorities in Wales, either outright or as the largest party, and Bridgend Council leader Cheryl Green said she and her colleagues in Cardiff, Swansea and Wrexham were all opposed to a deal with Labour.
From 2000-2003 there was a Lab-Lib Dem coalition in Cardiff Bay
"I would be adamantly against any Liberal Democrat-Labour administration," she said.
'Listening to views'
"To prop up a party that is clearly on the decline would be dangerous. We've had a brief meeting and obviously we are seeking further meetings on this."
She said Mike German, leader of the Lib Dem AMs, knew how they felt. "Mike is by no means in the dark about this at all," she added.
North Wales AM Ms Burnham, asked if she agreed that propping up Labour was dangerous, said: "We have to take every point of view on board and I think it's extremely important for us to be very sensitive to the needs of all the councils.
"The councils that we lead are doing extremely well. In the former Labour days the papers were full of anti-council rhetoric and you'll find that the councils led by Liberal Democrats are listening to people's views as best as possible."
The leadership of Mr German - who was Rhodri Morgan's deputy first minister in the coalition government - has also been questioned.
Lib Dem South Wales West AM Peter Black said his party had to examine its performance and "if we decide that part of that process involves a change of leadership then we have to look at that."
Asked if she had confidence in Mr German, Ms Burnham replied: "We have to discuss that today".
Pressed on the issue, she said: "We have to do better than last time, when people like myself didn't have the opportunity to express a view".
Plaid Cymru is the second biggest party, with three more seats taking it to 15. Plaid leader Ieuan Wyn Jones said an agreement with Labour was a possibility, but with strict conditions.
Mr Jones said: "We wouldn't agree to prop up a Labour government that had lost an election by having a day-by-day informal agreement.
"That produces instability - you can't have a long-term programme. That is out, but anything else which includes a policy agreement based on principles in the interests of the people of Wales you have to look at."
'Repent at leisure'
Labour's Andrew Davies, who was enterprise minister in the last assembly government, said his party would need to take stock.
"If we rush into something we could repent at leisure," said Mr Davies.
"We need to bear in mind what's in the best interests of Wales and the people of Wales and not local or sectional interests."
BBC Welsh affairs editor Vaughan Roderick said he thought the instinct of Mr German was to do a deal with Labour, but most of his party was opposed.
But he pointed out that a deal with the Lib Dems would still give the assembly government only 32 AMs, which required "iron discipline" from the two parties for four years.
However, any kind of Labour agreement with Plaid would be "loathed" by some members of both parties.
Any Plaid deal with Labour would involve big concessions from Labour leaders both at Cardiff Bay and Westminster on increasing the assembly's powers and changing the way Wales is funded from the UK government.
He said the option of a Labour-Plaid deal remained open but it would be "expensive" for Labour, and would be difficult because of the "tribal loathing" between the two parties.