Some have argued that Republican voters held their noses and voted for Trump because, while odious, issues dear to their hearts like religious freedom, or abortion, or taxes compelled them to make such a choice. But there’s no evidence a large number of Republicans object to Trump’s discriminatory policies, or to his frequent attacks on black public figures. According to one recent CBS poll, while most Americans disapprove of Trump’s record on racial issues, 83 percent of Republicans approve. The vast, overwhelming majority of Republicans aren’t quietly disgusted with Trump, but grateful for Neil Gorsuch. When Trump calls black athletes who protest police brutality “sons of bitches” and demands they be fired, they’re not embarrassed. They like it. Trump knows they like it. That’s why he keeps doing it.
Given that, it’s hard to imagine that, even if a tape of Trump using the word nigger exists, it would substantially erode political support from his base. The idea that the word is some kind of red line that erases plausible deniability is an illusion. Every time Trump’s behavior violates some conservative value—from his alleged infidelity to his denigration of war heroes and gold-star families to his relentless crony capitalism— pundits predict his undoing, and Trump emerges unscathed. There’s no reason why many of Trump’s strongest supporters wouldn’t also be able to rationalize his use of a racial slur, especially given their enthusiasm for his culture-war provocations.
It’s possible that this time would be different, that a recording of Trump using a racial slur would meaningfully alter his supporters’ perception of him. But given this track record, it seems very unlikely.
The more likely outcome is the one that followed the recording of the president saying he likes to grab women “by the pussy.” Most Trump supporters easily acquiesced to the explanation that the remarks were mere “locker-room talk,” despite the more than a dozen women who said otherwise. This time, too, many would likely argue the tape is fake, or taken out of context, or that he’s being victimized by the political-correctness police. Or they’d simply change the subject. (Aren’t there lots of recordings of the Pulitzer Prize–winning artist Kendrick Lamar using the word? Checkmate, libs.)The only thing I'd underscore here is that there is a propensity in the media to simply refuse to believe that sizable portions of the Republican base is racist. I think this stems from a lingering anxiety about being part of the "liberal media", all coastal elite-ish and out-of-touch with real America, and a corresponding skepticism about their intuitive instincts regarding the racial politics of middle White working class America. Sure, the most obvious reason for why they're attracted to Donald Trump is racism -- but that's such a mean thing to think! So media figures scramble about for alternative explanations that seem less judgmental and hostile -- hence how we've gotten years of "economic anxiety" narratives that just aren't backed by the data.
But the fact is, by and large Republicans like Donald Trump on race. It was racism, after all, that caused him to emerge from the pack of Republican candidates in the first place. Unabashed racism is and always has been Donald Trump's comparative advantage over other high-profile conservatives. And the past several decades have been one long campaign by conservatives in rationalizing what one might have thought would be indisputable cases of bigotry -- they're pros at it at this point.
So no, I don't think a tape of Trump using the n-word will have more than a marginal and fleeting impact on Trump's approvals. The people who like him already know who he is. That's why they like him.