In the interview, Colbert asked Mr. Biden about criticism directed toward his son.
"What are you going to do and how will you sustain each other for the attacks you know are coming your way?" Colbert asked. "Case in point, I know you want to be as bipartisan and reach across the aisle, but as much as you don't want it to happen, you know that the people who want to make hay in Washington are going to try to use your adult son as a cudgel against you. How do you feel about that, and what do you have to say to those people?
"We have great confidence in our son," Mr. Biden told Colbert. "I am not concerned about any accusations that have been made against him. It's used to get to me. I think it's kind of foul play but — look, it is what it is. And, he's a grown man, he is the smartest man I know, I mean from a pure intellectual capacity. And as long as he's good, we're good."
Colbert responded: "As a father I understand that and I admire that. But I mean, in terms of your job as president, can you reach across the aisle to people who'll be using this as an attack on you when it is such a personal attack because it's about family?"
"But if it benefits the country, yes. I really mean it," Mr. Biden said. "Because we know who we are."
related to Hunter Biden's taxes comes after months of criticism of him from conservatives and the president's allies. Two sources familiar with the investigation have told CBS that the "tax" investigation began in 2018.
At the time the investigation was announced, Hunter Biden, 50, issued a statement saying he believes a review will "demonstrate that I handled my affairs legally and appropriately."
Colbert also asked Mr. Biden about Republicans who haven't yet acknowledged that he won the 2020 election.
"Look, they're in a tough spot," Biden said. "I know everybody says, 'Well, they should just step up.' How can I say this? A number of them sent messages to me four weeks ago: 'Give me time, Joe. Give me some time.' It's fine by me. It's fine by me. We won."
When asked specifically about Senator Lindsey Graham, Mr. Biden said that Graham has "been a personal disappointment, because I was a personal friend of his."
But despite the attacks that he and his family have faced, Mr. Biden said he's confident he'll be able to work with leaders on both sides of the aisle to better the nation.
"I'm gonna be judged by history on whether or not I can make things better for the American people," he said. "I will deal with anyone if what we're working on is improving the well-being of the American people. That's not phony, it's real. I'll swallow hard, and I'll do it."
This story has been updated to include Colbert's question to Mr. Biden about his son.