President Donald Trump is betraying his base by working with congressional Democrats to protect from deportation the 800,000 young unauthorized immigrant DREAMers who were largely brought to America as children.

That, at least, is the story as interpreted by voices ranging from NPR to conservative provocateur Ann Coulter to hardline immigration restrictionist Rep. Steve King (R-IA) to Breitbart, which dubbed the president “Amnesty Don” in a recent headline.

@RealDonaldTrump If AP is correct, Trump base is blown up, destroyed, irreparable, and disillusioned beyond repair. No promise is credible. https://t.co/uJjxk6uX5g — Steve King (@SteveKingIA) September 14, 2017

There’s just one problem with this narrative: It’s wrong. In fact, despite the positions of some prominent conservative voices, at least one poll suggests that the actual voters who constitute Trump’s base support finding some way to protect the DREAMers — whose lives, it should be noted, Trump initially jeopardized by sunsetting President Obama’s Deferred Action for Childhood Arrivals program in early September.

William Galston of the Brookings Institution sums up the evidence in a piece published on Friday:

A Politico/Morning Consult survey .... found that 58 percent of Americans want the Dreamers to be allowed to stay in the United States and become citizens if they meet certain requirements. An additional 18 percent think the Dreamers should be allowed to become legal residents but not citizens. Only 15 percent think they should be removed or deported. The breakdown of the 76 percent who want the Dreamers to remain either as citizens or permanent legal residents is revealing. It includes 84 percent of Democrats, 74 percent of Independents, 69 percent of Republicans — and two-thirds of self-identified Trump voters. 60 percent of the voters who “strongly approve” of Mr. Trump’s performance as president want the Dreamers to be allowed to stay, compared to 33 percent who want them to be deported.

Since Trump announced he was ending DACA, the polling has clearly been in the DREAMers’ favor. Just 12 percent of independents and only 24 percent of Republicans believe they should be deported, according to one poll cited by Politico; Trump, of course, won 89 percent of Republicans in the 2016 election.

Trump’s base does hold positions on race and immigration that put its members far to the right of the rest of America. According to Pew polling, Trump supporters are far less likely to believe immigrants improve America, say undocumented citizens are less hardworking and less honest than American citizens, and, unsurprisingly, overwhelmingly support building a wall along the Mexican border.

But the DREAMers — who, their defenders note, were brought to America often through no fault of their own — are a particularly politically sympathetic constituency. Trump working with Democrats to protect them thus isn’t a sign that he’s breaking with the immigration views of his base; it’s instead a suggestion that he’s in tune with it.