The emphasis in that sentence could turn out to rest squarely on 'might' and 'a bit'. History shows that managers of big clubs who cannot even wring a drink of water out of matches like this do not survive very long.
It was not merely that Everton were bad in this 2-0 defeat, although both goals confirmed that their defence is capable of being very bad indeed. The side have also become terminally unlucky, and the temptation to draft in somebody who might bring some luck with him is becoming irresistible.
The Everton chairman, Peter Johnson, stopped short of the dreaded vote of confidence when he loomed in the interview-room doorway like the harbinger of doom.
Walker also seems to retain the trust of a sizeable section of the crowd.
The numbers at the Gwladys Steet end who chanted his name at the end of another defeat were more impressive than the few who called for his sacking outside, accompanied by a lone piper, playing the Z Cars theme at the tempo of a lament.
Walker's entry on to the pitch at the end to acknowledge the crowd and shake hands with each of his players was easy to misinterpret as a leave-taking.
His own explanation was that he was telling the players 'to get their heads up' and that the least the long-suffering spectators deserved was recognition of their loyalty.
Walker admits that what they also deserve is a side rather better than four points adrift at the foot of the table. The introduction of Duncan Ferguson and Iain Durrant, both of whom had promising home debuts, is at least evidence that the club are trying to give them that.
But then so was the purchase of Daniel Amokachi, who is now beginning to cut a sorry figure. The Nigerian runs around with undiminished enthusiasm and consistently looked the part, but any doubts about how he would integrate at the club have been stilled by his very Evertonian strike rate of one goal in eight matches.
The contrast with Dion Dublin, who twice almost claimed the distinction ahead of Amokachi of becoming Everton's first high- profile black player, was instructive.
The Coventry striker is never going to look pretty, but Saturday's stunning overhead volley made it seven goals in eight starts for his new club and he is playing with unlimited confidence.
There was nothing pretty either about the Coventry defensive effort in the second half, but the heavily manned rearguard marshalled by the unsung David Rennie and David Busst was far more effective than yet another rearrangement of the furniture in Everton's defence.
Goals: Dublin (7) 0-1; Wegerle (18) 0-2.
Everton (3-4-1-2): Southall; Jackson, Ablett, Unsworth; Horne, Parkinson (Stuart, 77), Samways, Burrows; Durrant; Amokachi, Ferguson. Substitutes not used: Rideout, Kearton (gk).
Coventry City (4-4-2): Ogrizovic; Pickering, Rennie, Busst, Morgan; Flynn, Darby, Cook, Jones; Dublin, Wegerle. Substitutes not used: Burrows, Quinn, Gould (gk).
Referee: D Elleray (Harrow).Reuse content