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And sources said some Labour councillors, furious at any concession to the Conservatives, could even refuse to back their own party's attempt to win power at Thursday's full council meeting.
The Lib Dems agreed on Tuesday night to vote for a minority Labour administration as an alternative to the proposed SNP-Green coalition in return for three “non-political” posts, including licensing board chair. But Tory votes would also be needed for Labour to secure power on Thursday.
Sources say the Labour group had earlier specifically ruled out any posts for Tories. The thinking was they would opt to back Labour anyway because the only alternative was to abstain and allow the SNP and Greens to take power.
However, sources said Councillor Day revealed at a Labour group meeting on Tuesday night that as well as the posts for the Lib Dems he had agreed to give the vice-convenerships of two "non-political" committees to the Conservatives.
One insider said Cllr Day had blamed the Lib Dems for the move. "He said the Lib Dems had demanded that security to support Labour."
The group voted to go ahead with the deal and seek to form a minority administration.
But the insider said: "The Labour group is extremely divided on this – very angry. I don't think we can guarantee that the 13 Labour councillors will support this. I don't think it would be accurate to say there will be a majority in the council on Thursday for this proposal.
"At no point, at any meeting, up until Tuesday night was there any proposal to give jobs to Tories and in fact at the previous group meeting there was an amendment to the proposal saying there would be no jobs for Tories."
The Lib Dems said it was “not true” that there was any demand from them that the Tories should be given jobs. A Lib Dem source said: “It’s entirely a matter for the Labour party to decide what they put forward. Our decision on how to vote was not dependent at all on any positions being offered, or not, to the Conservatives.”
As well as licensing board chair, Lib Dem councillors will be appointed as conveners for the regulatory committee and development management sub-committee, which decides planning applications.
The SNP has 19 seats on the council, Labour 13, the Lib Dems 12, Greens 10 and Tories nine. Labour’s deal with the Lib Dems and the Tories does not go beyond their support to win control. There is no agreement for them to back any policy proposals. And all the key posts in the administration will be filled by Labour councillors.
SNP group leader Adam McVey said his party was by far the biggest. “If we are forced into opposition by parties undermining the election outcome, we will use our weight in the chamber to hold all three parties to account for the actions of a Conservative and Liberal Democrat-supported administration, on their policies and on what they deliver for our residents.”