Unison branch secretary John Sharman has written to all members of the council urging them to vote against the Conservative group head becoming leader of the council in a ballot today.
The council has been in the headlines over a string of unlawful decisions. An auditor's report accused Mr Speechley of abusing his power, intimidating officers and making illegal decisions (LGC, 10 May).
Mr Speechley was re-elected by the Tories by 25 votes to 12, out of 49 councillors. Those 12 could swing the vote away from him at today's meeting of all 76 members.
He added: 'I have never tried to influence such a vote before, but it would be a dereliction of my duty if I did not do so now.'
He warned: 'Staff have a sense of disbelief that the organisation can continue in its dysfunctional state. Staff go on serving but their morale is in tatters.'
Lincolnshire CC member and leader of South Holland DC, Eddie Poll (Con), has broken ranks to admit 'the county council has become dysfunctional and the object of criticism and ridicule'.
Labour group leader Robert Parker said if the national Conservative Party does not step in, it will remain 'essentially the party of sleaze'.
Mr Speechley said only 20 staff members attended Unison's meeting where the union decided to write the letter. He fully expected to survive today's vote.
He added: 'A lot of staff have said to me 'I hope you're not going to stand down, there is such a lot of good work going on'.'
The council's controversial moves have included:
--plans for an all-Tory scrutiny panel, later dropped (LGC, 22 December 2001)
--an 'unlawful'£150,000 payment to a business which re-routed its lorries away from a Lincolnshire village (LGC, 10 May)
--'unlawful' severance pay for two ex-officers totalling£410,000 (LGC, 10 May).