As Republicans were promoting themselves as a multiracial party from the platform in Tampa two weeks ago, an ugly incident on the convention floor suggested not everyone had got the memo. From the podium a range of speakers of Haitian, Mexican, Cuban and Indian descent spoke of how their parents had overcome huge barriers so they could succeed in the US. In the audience, a successful black woman who works for CNN was being pelted with peanuts by a convention-goer, who said: "This is how we feed the animals."

The tension between the projection of a modern, inclusive, tolerant party and the reality of a sizeable racially intolerant element within its base pining for the restoration of white privilege is neither new nor accidental. Indeed, it in no small part explains the trajectory of the Republican party for almost the last half century. In his diary, Richard Nixon's chief-of-staff, Bob Haldeman, described how his boss spelled out the racial contours of a new electoral game-plan to win southern and suburban whites over to the Republican party in the wake of the civil rights era. "You have to face the fact that the whole problem is really the blacks," Nixon told him. "The key is to devise a system that recognises that while not appearing to."

This could be the final hurrah for what became known as Nixon's southern strategy in what is shaping up to be the most racially polarised election ever. Black support for the Republican party literally cannot get any lower. A recent Wall Street Journal poll had 0% of African-Americans saying they intend to vote for Romney. At 32%, support among Latinos is higher but still remains pathetically low given what Republicans need to win (40%) and what they have had in the past – in 2004 George W Bush won 44%. As a result, the party of Lincoln is increasingly dependent on just one section of the electorate – white people. To win, Romney needs 61% of the white vote from a white turnout of 74%. That's a lot. In 2008, John McCain got 55% from the same turnout. "This is the last time anyone will try to do this," one Republican strategist told the National Journal. And Republican consultant Ana Navarro told the Los Angeles Times: "Where his numbers are right now, we should be pressing the panic button."

There are two main reasons for this panic. The first is that the "system" Nixon referred to is now recognisable by most – particularly with a black president in the White House. As people have become more attuned to the frequency of the dog whistles, the tone has necessarily become more shrill. During the primaries, Rick Santorum told a crowd in New Hampshire: "I don't want to make black people's lives better by giving them somebody else's money; I want to give them the opportunity to go out and earn the money." Newt Gingrich branded Obama "the food stamp president". Just a few weeks ago, in a clear nod to the "birthers", who insist Obama was not born in the US, the party's nominee, Mitt Romney, went to Michigan and joked: "No one's ever asked to see my birth certificate. They know that this is the place that we were born and raised." This is rhetorical peanut throwing. When everyone can hear it, you've transitioned from a dog whistle to a straight-up whistle.

Second, with white people destined to become a minority in a few decades, the strategy is no longer an anchor but a millstone. Tying Republican fortunes to the white vote made electoral sense in the early 1970s. Since 1980, the white share of the electorate has fallen in every consecutive election bar one – 1996, when Ross Perot ran. The more black and Latino voters the Republicans alienate, the more white voters they need to replace them. The trouble is they are fishing for a larger number in a smaller pool, which demands ever more juicy bait. "The demographics race we're losing badly," said Senator Lindsey Graham, acknowledging the problem. "We're not generating enough angry white guys to stay in business for the long term."

But that's not for want of trying. In just one example, the New York Times' Thomas Edsall analyses a Romney ad lambasting Obama's healthcare reform. The ad states: "You paid into Medicare for years – every pay check. Now when you need it, Obama has cut $716bn from Medicare. Why? To pay for Obamacare. The money you paid for your guaranteed healthcare is going to a massive new government programme that is not for you."

Leave aside the fact that the ad is judged by Politifact as only half true and that the Republican vice-presidential candidate Paul Ryan has proposed a budget that would cut a similar amount from Medicare without healthcare reform. More than three-quarters of Medicare recipients are white; more than half those without health insurance are not white. By linking the two in this way, "Obamacare" thereby becomes a transfer of resources from hard working white retirees to indigent minority ethnic people. Meanwhile, Larry McCarthy, who produced the now infamously racist Willie Horton ad for George HW Bush's campaign in 1988, is working for one of the Super Pac's backing Romney.

Describing the evolution of the Republicans' racial appeal, the late Lee Atwater, one-time chair of the Republican National Committee and member of the Reagan administration, said in 1981. "You start out in 1954 by saying, 'Nigger, nigger, nigger'. By 1968 you can't say 'nigger' – that hurts you. Backfires. So you say stuff like forced busing [and] states' rights. You're getting so abstract now [that] you're talking about cutting taxes, and all these things you're talking about are totally economic things and a byproduct of them is [that] blacks get hurt worse than whites … obviously sitting around saying, 'We want to cut this' is much more abstract than even the busing thing, and a hell of a lot more abstract than 'nigger, nigger'."

Reflecting on her experience in Tampa, Patricia Carroll, the CNN camerawoman who had peanuts thrown at her said: "I can't change these people's hearts and minds … This should be a wake-up call to black people … People were living in euphoria for a while. People think we're gone further than we have."

Twitter @garyyounge