Mr Mears' declaration that allegations of prejudice were "nonsense" at the conference earlier this month is likely to go down as a turning point in a chequered 10 months as leader of the society's 70, 000 solicitors.
The figure being strongly tipped to stand against him for the presidency is Tony Girling, a Kent solicitor and long-standing member of the society's 75-strong ruling council and the current deputy vice-president.
While neither Mr Girling nor any of the other names circulating for the vice-president and deputy vice-president posts are expected to declare their hands until nearer the 5 June deadline for nominations, a group of strategists is expected to formally announce in the next few weeks a "grass-roots" movement to identify challengers.
The object is to counter Mr Mears' claim that only he stands for the small and medium-sized firm that has taken a hammering during the property slump. Mr Girling's firm operates a series of small offices. In reality, the move to get rid of Mr Mears and Mr Sayer is likely to garner significant support from within the council.
The pool of names from which other contenders for the three key posts might be drawn include Michael Napier, a high-profile personal injury lawyer and Lesley MacDonagh, managing partner of the city firm Lovell White Durrant. Eileen Pembridge, who came third in last year's contest, has also said she would consider standing for election if other contenders did not come forward.
Mr Mears took the society by storm last summer after forcing a contested election for president for the first time in 40 years and then winning it on promises of higher conveyancing fees.
But alarm bells began to ring when he used his maiden speech to denounce the "discrimination industry", followed by a string of opinions often at odds with long-considered Law Society policy. An exodus of staff has begun at the society's headquarters in Chancery Lane, central London.
His future as the profession's leader could have been sealed at the women's conference, when he outraged an audience of solicitors and barristers by denying the existence of sex discrimination in the profession and lambasting discrimination "zealots" who thrived on "grievances and heresy-hunting and use minorities as raw material for their whinge factories".
Ironically, Mr Mears was recently forced into defending existing Law Society policy on conveyancing fees, following the formation of a breakaway Solicitors' Association which is demanding an end to predatory pricing. Writing in the profession's journal last week, Mr Mears said: "An excellent idea. But how exactly?"
Leading article, page 16