Sen. Cory Booker on endorsing Hillary Clinton, new book

After a big loss in New Hampshire, Hillary Clinton is depending on her closest allies to galvanize support - among them, Sen. Cory Booker of New Jersey.

Booker, who has been front-and-center for Clinton in the early primary states, said the results did not take him by surprise and that Clinton herself had expected a "hard-fought campaign."

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"We knew that Vermont is Bernie [Sander]'s state, so New Hampshire is his backyard and that she was going to have a tough time. It would be a real stretch to win that," Booker told "CBS This Morning" Friday. "But now we're going into a very diverse part of our nation where the Democratic base is really represented in every element and I think she's going to be strong."

Still, a CBS News poll found a huge gap between Clinton and Sanders' appeal to voters under age 30. Clinton trailed Sanders among that demographic by 67 percent in New Hampshire and 70 points in Iowa.

Booker responded to the numbers, calling them a "reaffirmation" that the race to become president is "not easy." Citing several political hurdles Clinton has encountered throughout her career - from her days in Arkansas, as first lady and as senator -- Booker expressed confidence in her ability to succeed.

"Every time she's been counted out, she's risen to a new level of service," Booker said.

While Booker has been vocal about his Clinton endorsement, he does not want bipartisanship to take a back seat. He is proud to call prominent Republicans like Rand Paul and Chris Christie his partners on issues where they can agree. In his new book, "United: Thoughts on Finding Common Ground and Advancing the Common Good," Booker details why he values that approach.

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"We've gone far as a country because we've understood that our differences and our disagreements matter, but our country matters more," Booker said.

But Booker said the responsibility to fix the divisiveness in the country goes beyond Washington. Booker gets personal about his own mistakes and lessons, which he hopes will inspire others to take responsibility.

"I wanted to write a book that was like 'Let's be naked,' in a sense about my failings, about my faults when I got it completely wrong and when I met people who taught me how to get it right," Booker said. "So I'm hoping this understands that we can't just point to one problem and say we're too divided. If we want more unity, we have to be more united. If we want more hope, we've got to be engines for that hope."