Many Americans in the middle of the country will become "politically frustrated" and have their "hopes dashed" if the economy and wages don't significantly improve, as President Trump has said they will, "Hillbilly Elegy" author J.D. Vance told CBS News' "Face the Nation" in an interview airing Sunday.

Mr. Trump emphasized the importance of jobs in the life of a community, something that spoke to working people in a way Republicans had not before, said Vance, who grew up in rural Ohio and eventually graduated from Yale Law School. "Hillbilly Elegy: A Memoir of a Family and Culture in Crisis" released in June 2016, doesn't mention Mr. Trump. But it does depict the disaffection felt by America's working class -- by many "people living in a certain part of the country, people from a certain demographic segment who did overwhelmingly support the president" in 2016, Vance said.

"When the president talks about tax reform, he talks about the people who will benefit," Vance told CBS News Chief White House Correspondent Major Garrett. "He talks about American jobs. He talks about the fact that we're going to be taking money that's overseas and bringing it back to the United States so that it will employ American workers. I think that focus again on the American working and middle class is- is-is to me the most thoughtful and, in some ways, the most genius part of Trump's approach to politics."

But, if the president's rhetoric and those voters' expectations don't match -- if life doesn't significantly improve -- that could lead to political frustration and dashed hopes for many Americans outside of economically thriving cities in say New York or California, Vance said. Vance said that's certainly a "political concern" for the Trump administration, but it's also a concern for Americans.

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"It's a concern for a lot of folks who really do expect things to get a whole lot better," Vance said. "One of the things I really worry about is that if you don't see middle class wage growth, if you don't see the economy in certain areas of the country, the middle part of the country, starting to come back in the same way that it's doing especially well, let's say, in California or New York, then people are going to become politically frustrated."

"But more importantly, they're going to have a lot of hopes dashed," Vance added. "This sense that maybe this is the moment, this is the electoral moment where a lot of our fortunes turn around, that -- that's going to disappear. And consequently, folks are going to be pretty upset about it."

Vance's interview with Garrett airs on "Face the Nation" Sunday morning.