You’d think it would happen all the time. Given how often they’re drawn from different parties, it should be routine for the US House of Representatives to condemn the president. In fact, it’s rare. Until last night, the House had not made that formal move since it admonished William Howard Taft more than a century ago. So Donald Trump has earned himself yet another place in the history books, rebuked by the House late Tuesday night for telling four members of that body – all women of colour, three of them born in the US and all American citizens – to “go back” to where they came from.

For anyone opposed to prejudice and bigotry, the moral argument for the resolution is unassailable. Not many would want to dispute the text’s contention that “President Donald Trump’s racist comments ... have legitimized and increased fear and hatred of new Americans and people of color.” That is little more than a statement of the truth. Proof came swiftly, when presidential adviser Kellyanne Conway referred to the four Congresswomen as “the dark underbelly” of America and, following a question about the issue during a press huddle, immediately asked the (Jewish) reporter who had asked it, “What’s your ethnicity?”

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Trump himself might claim that he “does not have a racist bone in his body”, using that curious anatomical formulation so often deployed by bigots when exposed. But his words speak for themselves, and they are a textbook example of racism. As Alexandra Ocasio-Cortez, one of the four women targeted by Trump put it: “You’re right, Mr President – you don’t have a racist bone in your body. You have a racist mind in your head, and a racist heart in your chest.”

Indeed, as anyone watching Netflix’s When They See Us – telling the story of the five innocent African-American boys wrongly convicted in the notorious Central Park jogger rape case in 1989 – can testify, Trump’s racism is decades-old. The series recalls how Trump weighed in at the time, taking out newspaper ads calling for the death penalty. He still insists on the teenagers’ guilt, even though the convictions were overturned long ago.

So the principled case for denunciation is strong. What though of the politics? At first glance, the rock-solid unanimity among Democrats looks like good news for the party, which has been badly divided. There’s been tension between House Speaker Nancy Pelosi and the so-called “squad” of four congresswomen, who many veteran Democrats consider too leftwing, too woke and too quick to grab the media, and social media, spotlight for themselves rather than serving their time as team players. At a stroke, Trump’s tweet has healed that rift. Suddenly, Pelosi is shoulder-to-shoulder with AOC, Ilhan Omar, Rashida Tlaib and Ayanna Pressley. Rather than letting Democrats tear each other apart, and enter the 2020 election divided, Trump has brought them together.

And yet that superficial setback for Trump conceals his larger strategic objective. He has reportedly told aides that he is delighted that Democrats are closing ranks, because that’s what he wants: to “marry” Pelosi to the squad.

Put simply, he wants to choose his opponent for 2020. He doesn’t want the face of the Democrats to be Joe Biden, Elizabeth Warren, Kamala Harris or Pete Buttigieg. He wants it to be a composite of AOC, Omar, Tlaib and Pressley. That’s partly because he reckons the squad’s politics are out of step with the US mainstream – that he can easily cast them as radical socialists with terrifying views. But mainly it’s about race (with a dash of misogyny for good measure).

Trump’s calculation is that he can repeat in 2020 what he did in 2016, winning an electoral college majority by winning in Michigan, Wisconsin and Pennsylvania – and that he can edge a victory in those states by appealing to white voters stirred by racial resentment. Rather than trying to appeal to moderates and independents by boasting of, say, low unemployment and good economic numbers, he’d rather pull in yet more of the demographic that already favours him: white, often male, former Democratic voters without a college education. And he thinks he can do that by getting AOC’s or Omar’s face on the news every night.

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It’s race-baiting, no doubt about it. But it might also be effective, as Trump’s 2016 campaign proved. The result is a dilemma for Democrats. Do they try to win back those white, low-income voters who supported Trump last time or do they use the president’s hateful behaviour, including his attacks on the squad, to drive up turnout among those appalled by it – especially black voters and young people?

Last night’s House resolution, with Democrats standing foursquare behind the four women, has pushed them down the latter track. Which is just what Trump wants. As far as he is concerned, he set a trap and they walked right into it.

The conundrum for Democrats is similar to the one they face over impeachment. Their moral duty is clearly to hold the president to account for his violations of the constitution. But the political cost will be high, and the effort will almost certainly be futile. That much was demonstrated again last night. Remember, Trump can only be removed from office by a two-thirds vote of the senate, which will require Republicans to turn on him. Only four of them did so in the House resolution. The grim truth is that, no matter how racist his behaviour, no matter how much he abuses his power, Republicans belong to Trump now. He owns them.

The result is that Democrats face a choice between doing what is morally right and what is politically smart. When you’re dealing with an amoral bigot in the White House, those two things are not always the same.

• Jonathan Freedland is a Guardian columnist