I know that Barack Obama is incredibly smart, and it's not that I'm surprised that he gave a fantastic speech. But I've been following American politics for a long time, and sometimes you see something that works on so many levels that you kind of have to gasp at its sophistication.

This speech marked a sharp line in the sand, breaking overtly with the past administration. That message was clear and intentional. It is a much more confrontational approach than ­inauguration speeches have typically been in America. I am overjoyed.

I thought Obama did three things impressively. Firstly, he sounded a note of our dire circumstances that was in line with a reality that many have been in denial about. That is technically ­brilliant, because he's inheriting a mess, and he's telling people, "We're not going to dig ourselves out of this easily." But also, "Don't blame me for it all."

The second was that he reasserted the primacy of the constitution and the rule of law. With Bush sitting behind him, that was like showtime at the OK Corral. I have written in the past that it is going to take a grassroots movement to support him in reasserting the rule of law, because there are so many vested interests that stand opposed to it. But that was a shot across the bows.

Thirdly, most amazingly, I feel that he dialled down the threat level of the US with just a few sentences. He reached out a hand to the Muslim world. For Obama to say, "I'm not going to demonise you" – that is extraordinarily stabilising.

On top of all that, he gave plenty of red meat to the right, honouring the ­military and their sacrifices. The choice of the conservative, anti gay-marriage pastor Rick Warren to pray sent a message to the conservative base of the opposition that this is going to be a values-based presidency, that he's not going to dismiss the substantial proportion who opposed Democrats not because they disagreed with their economic policies, but because they disagreed with how amoral our policies have often been presented as being. It is not how I would wish for things in an ideal world. But Obama is playing poker brilliantly, because he has handed over something that is not very valuable. And he did all of this without a single partisan sentence. He spoke about Republican policies, but not Republicans. He isn't missing a trick. I thought it was a home run.

The great leaders in the US weren't the cheerleaders who promised ­morning in America. They were the ones that forced us to look in the mirror. Since Reagan there has been this tradition, which has become a cliche, of promising morning in America, this fake optimism, we're the best, the city on the hill.

In fact the great American task is self-scrutiny. Abraham Lincoln gave speeches about the civil war in which he said, in essence, "We've brought this on ourselves by enslaving Americans." Obama's speech was a diagnosis: "We have to take steps to rebuild our nation." I'm not saying, "Hooray, he offered a tough, dark recognition of our reality." I'm saying "Hooray" because he has recognised that the only way to save America is to confront it.

Naomi Wolf is a feminist, author and former political consultant to the Clinton administration