Iain Duncan Smith has gained another seven months to prove himself a vote-winner for the Conservatives or face the prospect of a direct challenge to his leadership, according to shadow cabinet colleagues.

His next big test will be the May council elections, in which the Conservatives will be defending gains they made in the local elections of 1999, which was the high watermark of William Hague's tenure as party leader.

After last week's party conference in Bournemouth one shadow minister said: "We have stepped back from the brink. People have given him a bit more time to prove himself. We hope he'll use that time more effectively."

But he warned that the Conservatives will need to increase their number of council seats in May, or MPs will start to ask whether they would be better off with a new leader. Tory MPs will be nervous of any sign of their votes slipping away to the Liberal Democrats in the shires.

Five members of the Shadow Cabinet – the shadow Chancellor Michael Howard, shadow Deputy Prime Minister David Davis, party chairman Teresa May, shadow Home Secretary Oliver Letwin and shadow Transport Minister Tim Collins are all vulnerable to small swings to the Liberal Democrats

Another shadow minister, more hostile to Mr Duncan Smith, described his speech to the conference as "badly delivered and over-rehearsed" and forecast that a poor result in May would trigger a leadership contest in which many MPs who previously backed right-wing candidates would swing behind the former chancellor Kenneth Clarke.

Mr Duncan Smith was given a warning about the threat to his leadership from his predecessor as MP for Chingford, Norman Tebbit. It was clear by yesterday that Lord Tebbit has seen off modernisers who wanted to expel him from the party, in a gesture equivalent to Tony Blair's decision to rid the Labour Party of Clause 4 of its constitution.

Interviewed in yesterday's Daily Telegraph, Lord Tebbit claimed: "They know that if they could persuade Iain Duncan Smith to expel me from the party that it would be the end of his leadership. He'd lose several members of his Shadow Cabinet, he'd lose a number of frontbench spokesmen in the Lords and I can't vouch for what would happen in Chingford."

Lord Tebbit, who bitterly opposed Michael Portillo's leadership bid last year, has alleged that a group known as the Movement had been plotting his expulsion. One former Portillo supporter, now in the Shadow Cabinet, said: "Norman Tebbit assumes that if two people get together and say 'Norman's a pain' this is a conspiracy. I've never even heard of this 'Movement'. It's just paranoia."