Gordon Brown has not come up a great deal in the American primary campaign, but he did during last week’s Democratic debate in Las Vegas, Nevada. Senator Hillary Clinton brought him up.

It was the second time she’d mentioned our prime minister, actually. The first was on the eve of the New Hampshire primary. And here’s how she put it: “I don’t think it was by accident that Al-Qaeda decided to test the new prime minister Gordon Brown immediately. They watch our elections as closely as we do, maybe more than some of our fellow citizens do . . . So let’s not forget you’re hiring a president not just to do what a candidate says during an election. You want a president to be there when the chips are down.”

In Nevada, she put it slightly differently: “I do feel that the next president has to be prepared because we are up against a relentless enemy. And they will take advantage of us.”

What was she getting at? It’s pretty obvious. She is predicting that electing her Democratic rival, Barack Obama, will invite a terror attack because he has less experience than she has. If you wonder if you’ve heard that kind of argument before, you have. It has been a staple of hardball Republican politics for the past seven years: vote for the Democrats and the terrorists win.

But Clinton deftly purloined it for her own purposes, pivoting a classic Karl Rove tactic against one of her opponents. Rove, you might remember, was chief political adviser to President George W Bush and the strategist in charge of his reelection campaign.

Ever since the Clintons’ near-death experience in the Iowa vote, their campaign has been playing a very Rovian game. The use of the politics of fear is just the start. In fact classic Rovian tactics are now at the heart of the Clinton campaign.

First, play to your base. Obama continues to appeal beyond core Democrats to independents and even a surprising number of disenchanted Republicans. Clinton decided, in response, to craft her appeal directly to core Democrats: public sector employees, the elderly, working women, the urban middle class. She constantly reminds people that she remains a lightning rod for Republicans. She also retooled her message to focus on the economic concerns that are becoming paramount in the race.

Second, attack your opponent on his strong point. Against a bemed-alled Vietnam veteran in John Kerry, the Bush campaign in 2004 employed surrogates to claim that Kerry didn’t deserve the medals and was actually an enemy of the troops. In the end, under Rove’s guidance, the president who avoided military service ran as more pro-military than the man who actually risked his life for his country.

Obama’s biggest strength among Democrats is his early and clear opposition to the Iraq war. And so, following Rove’s golden rule, Bill Clinton dismissed Obama’s long opposition to the war as a “fairy tale”. Because in 2004 Obama had refrained from criticising Kerry’s pro-war vote, Clinton argued that Obama implicitly agreed with it. Because he had voted – like so many others – to continue funding the troops, Obama was no different than Hillary. It didn’t work. But it was a classic Rove try.

Third, wedge issues. Rove’s classic example was same-sex marriage; a way to pit one largely Democratic constituency – gays – against others, namely socially conservative white ethnics and blacks. Hillary Clinton’s task in a Democratic primary is much trickier. But gender and race remain potent political tools for the unscrupulous. And she has used both.

She lost women to Obama in surprising numbers in Iowa. So how to heighten gender tensions to her advantage? Earlier in the campaign, she had put out a positive message of breaking the glass ceiling. But she also included blatant appeals to gender. When Obama and her other Democratic rival John Edwards both criticised her in her first bad debate performance, her surrogates put out word that they were “boys” “piling on” a female candidate.

As she looked like losing in New Hampshire, she adopted the persona of the badgered woman, unfairly attacked, yet struggling through like so many others. The now-famous emotional incident worked. The Democratic gender gap – previously small – widened dramatically in her favour.

Then there was simple sleaze. The Clinton campaign kept reminding people that Obama had not been “vet-ted”. Her pollster brought up Obama’s cocaine use on national tele-vision. Her New Hampshire campaign chairman also raised the drug issue. Two staffers were caught sending out e-mails accusing Obama of being a closet Muslim. Last week a blizzard of e-mails appeared on Jewish lists accusing Obama of being fond of the notorious black antisemite Louis Farrakhan.

Again, classic Rove tactics. You never personally make any claims against your opponent, but you sit back as surrogates put out sleaze by e-mail or insinuation. Then you decry the rumours while privately fanning them. Hey, it worked for Bush against fellow Republican John McCain in 2000.

Finally, the real toxin: race. The Clintons must have known this was an extremely risky gambit. Any crude attempt to exploit fear of a black candidate would have been terribly damaging to their campaign and legacy. My own sense is that Hillary Clinton’s initial gaffe – implicitly analogising herself to Lyndon Johnson and Obama to Martin Luther King – was an accident. She meant to make the point that she is a doer and he is merely a speaker. But inevitably it came off as condescending – as if black people always need white leaders to gain their own rights.

But once this was out of the bag, the Clintons decided to run with it. Their calculation was that simply by forcing Obama to become the “black candidate” they would neutralise his postracial appeal. They would polarise the base electorate into blacks and whites, make Obama look more like Jesse Jackson, and so pick up enough white and especially Hispanic votes to win.

The Hispanic vote is particularly important to Clinton. The campaign faces a key challenge in Nevada and may be decided in California. If she can gain antiblack Latino votes, she wins.

The Chicago columnist Don Rose explained the logic clearly enough: “They’re not really racists, they just want to stress that Obama hasn’t really transcended race and that a person of colour may not be electable. Think about it, folks. Over and over again.”

The hardball tactics of Rove have defined American political life for a long time. The Clintons have now shown they have learnt from the master. The question for the Democrats is whether they want a candidate who can play the Rove game as cynically and as brutally as the Republicans. Or whether they want a new start and a new politics.

That’s what is at stake now in the Democratic race. And one side has shown its true colours.

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