Steve Bannon tried to woo head of teachers' union -- and made an enemy for life CEO Steve Bannon speaks to '60 Minutes' (Screen capture)

Ousted White House chief strategist and "alt right" provocateur Steve Bannon tried to win over Randi Weingarten -- president of the American Federation of Teachers -- last January in an attempt to build a coalition to back his $1 trillion infrastructure plan.

According to The Intercept's Rachel M. Cohen, Weingarten's interaction with the CEO convinced her that she'd looked into the eye of a new foe.

"I came out of that conversation saying that this was a formidable adversary,” Weingarten told The Intercept.

Weingarten -- a Jewish lesbian who heads the first labor union to endorse Hillary Clinton in 2016 -- was concerned about the Trump administration's proposed education cuts in early 2017 when a mutual friend offered to set up a meeting between her and Bannon.

“Look, I will meet with virtually anyone to make our case, and particularly in that moment, I was very, very concerned about the budget that would decimate public education,” Weingarten told Cohen. “I wanted it to be a real meeting, I didn’t want it to be a photo-op, so I insisted that the meeting didn’t happen at the White House.”

She met with Bannon over dinner and the two had a wide-ranging conversation about "education, infrastructure, immigrants, bigotry and hate, budget cuts … [and] about a lot of different things.”

Bannon tried to recruit Weingarten to his polemic ideas about realigning the two major parties, she said.

“I think he sees the world as working people versus elites. And on some level, he’s thought about educators as working-class folks. But what he doesn’t do is think about the other side of educators, as people who fiercely believe in equality and inclusion. It isn’t an either/or philosophy. The [Martin Luther] King philosophy of jobs and justice is not the Bannon philosophy, let’s put it that way,” Weingarten explained. “He’s trying to figure out where the friction is, and how to change the alignment. I think that’s really what he was trying to do.”

Weingarten said he was even persuasive on some points, particularly his denunciations of hedge funder Democrats who back the charter school system.

“He hates crony capitalism,” Weingarten said. “The same kinds of things [we say], you could hear out of his mouth, and that’s why it’s so — you sit there in a surreal way, saying, ‘How can you sit right next to all these elites?’”

Rather than be converted to Bannon's cause, however, Weingarten has become one of the Trump administration's most outspoken critics on a range of topics from education cuts to immigration to the appointment of wealthy charter school proponent Betsy DeVos.

Cohen noted that Bannon's "alt right" affiliation has both "propelled his rise and put a ceiling on it."

After the death of anti-racism protester Heather Heyer in Charlottesville, VA, the "alt right" has become one of the most toxic affiliations in the country.

Bannon reportedly is afraid that Trump's power is ebbing away as his legislative agenda crumbles and Special Counsel Bob Mueller's investigation closes in on the West Wing.

In terms of Bannon, Weingarten said, "This is one smart guy, but I was pretty clear with him about my criticism of the white nationalism philosophy.”

"At the time of the meeting," wrote Cohen, "the Trump administration had proposed slashing the federal education budget by 13.5 percent, a figure that would amount to more than $9 million in cuts. The White House also proposed cutting Medicaid by $800 billion, threatening school districts with funding they use to provide health and special education services."