Nick Clegg raised his game today. This was, by a considerable distance, the best and most effective speech he has given as Liberal Democrat leader. But, even more important, he raised his party's sights. It was just bad luck that he chose to speak at exactly the same time that Barack Obama came to the rostrum at the United Nations in New York.

The most striking line of his speech came towards the end. "Imagine," said Clegg, "a Liberal Democrat cabinet." What a thought, indeed – and Clegg only got away with saying it by making a little joke about the odd heated meeting. But the thought of a Liberal Democrat cabinet is not hard because it is so difficult to imagine particular Liberal Democrat MPs as ministers – though lots of sketchwriters will have fun with that one. What was really striking was the political audacity of this leap of the imagination. Not since David Steel's famous call to his party to "prepare for government" has a leader of the third party tried harder to face his party with the thought of power than Clegg did in Bournemouth today.

This was a serious, ambitious speech. It started with a big, grown-up theme – Afghanistan – and a threat that withdrawal may be on the cards before long. Not an Iraq Mk II election-winner for the Liberal Democrats, perhaps, but definitely a clearer alternative policy – do it properly or do not do it at all – than the Conservatives will dare to outline in Manchester next month.

The bigger domestic theme – lifting the party's eyes to the possibility of power, and even of election victory – came next. "Let me tell you why I want to be prime minister," said Clegg. To many, this will seem foolhardy, almost juvenile. But if the Liberal Democrats are ever to be more than just a party on the parliamentary margins, while bigger parties decide who actually does the ruling, then Clegg has to imagine himself leading the country and Liberal Democrats have to imagine themselves running it.

There was a nice tight coherence to the main political argument of the speech. His syllogism went something like this: everyone wants change … Labour is incapable of change … The Tories offer an illusion of change … Only the Liberal Democrats can offer real change. "We carry the torch of progress now," was a good line – aimed directly at Guardian readers, one sensed.

To rouse a party for a general election battle in difficult times is a tough ask for a party leader who has only been in the Commons for four years. I thought Clegg did it well. There was a new confidence and maturity in this speech that wasn't there when he first spoke to a conference as party leader in Bournemouth last year. There were nice touches too – reminiscent, above all, (though the comparison will doubtless be unwelcome) of Tony Blair's self-deprecating style on such occasions. I liked the deft remark about his critic Evan Harris, and the confidence with which Clegg praised Vince Cable. Not every party leader – you know who I mean here – has the grace or generosity of spirit to give credible heartfelt praise to a colleague. But Clegg meant it.

Before Clegg spoke, the BBC showed an interesting preview of the speech by Charles Kennedy, his predecessor but one. Kennedy hasn't been Clegg's most loyal supporter this week. But he made several interesting points in his short film. A Liberal Democrat leader, Kennedy observed, has to play by different rules from the other party leaders. He has to live a little dangerously, take a few risks, attract some attention. This year, said Kennedy, Clegg has done that. He has found not just his feet and his voice as leader, but also his issues. He took risks, as when he called for the Speaker to quit.

Clegg has done that this week, too – though not in a way that Kennedy necessarily approved. He led from the front, telling his party that it was time for an end to shopping-list manifestos and time to start talking tough about cuts.

Clegg did it again in his conference speech. It certainly took risks. But it did two big things and did them well. It insisted that the Liberal Democrats are not just another variation on the same centrist party theme. And it said to the electorate that there are three choices in the general election of 2010. Clegg put it this way. There was exhausted Labour. There were the fake Tories. And there is real change in the form of the Liberal Democrats.

Of course, it's a bit of a stretch to believe that the election is really a three-party race yet. But that's what the leader's speech at a Liberal Democrat conference has to do. It has to make not just the party, but the country believe the improbable. Clegg gave it his best shot. In so doing, he came of age as a leading politician.