Mr Hague could face a leadership crisis if the party does not make significant gains in the European Parliament elections, which follow in June. Close allies admit privately he is still "on probation" amid growing doubts in the party about his performance.
An internal party memorandum, seen by The Independent, admits the Tories have slipped in polls since last autumn, when they fixed a goal of gaining between 700 and 800 seats in council elections.
Stephen Gilbert, the party's director of field operations, warns that the Tories will do worse than this if the council results reflect the latest opinion polls.
"We should be concerned that the results we would get based on these ratings are not as good as we thought we would achieve last October," he says in his memo to Michael Ancram, the Tory party chairman.
"We need to be aware that our chances of making the original 700 to 800 gains we believed to be a realistic target last October now looks tougher than we had anticipated. We need to be careful not to talk up our chances or we will face accusations of underachieving on May 6."
In the run-up to local polls in recent years, all parties have played down their prospects in the hope of winning favourable headlines after the results.
Labour is bracing itself for heavy losses in May because Tory fortunes were at a low ebb in 1995 when the seats being fought this year were last contested.
An internal Labour report suggests the party could lose 1,700 of the 6,000 seats it is defending if there is a repeat of last year's local authority results. The losses would rise to 2,400 seats if trends in council by-elections are repeated in May.
The Tories dismiss Labour's predictions as "nonsense" and academics believe losses of about 1,000 seats are more likely.
But the Labour document says: "It is impossible for the Tories to do as badly as this  again. A standstill from the 1988 local elections or even the general election would inevitably return to them many of the seats and some of the councils which they lost in 1995."
Greg Cook, Labour's polling expert, warns that Labour-run Sheffield is "very vulnerable" to a challenge by the Liberal Democrats, who have also made progress in Bristol and Chesterfield. He says the Tories will be looking to gain Trafford, while Labour could lose its overall majority in Basildon, Exeter and Portsmouth, which could become hung councils.Reuse content