Woodward, who is best known for his role in uncovering the Watergate scandal while at The Washington Post, published his latest book on the Trump presidency, "Rage," on Tuesday. He also authored the book, "Fear," which was released two years ago.
In the CNBC interview, Woodward compared Trump's early response to the intensifying coronavirus — which emerged late last year in Wuhan, China — to how former President George W. Bush responded immediately following the attacks on Sept. 11, 2001, that killed nearly 3,000 Americans.
"This happened in 9/11 after the terrorist attack in New York and the Pentagon. President George W. Bush actually gave speeches and said, you know, we're going to respond at an hour of our choosing," Woodward said, likely referring to Bush's speech at a national prayer service a few days after the attack.
"The public got behind this. The Congress got behind it," said Woodward, a two-time winner of the Pulitzer Prize, including an award as part of The Post's coverage of 9/11. "It was bad news. People won't flee from bad news. People in this country are problem-solvers, I believe."
Asked specifically by CNBC's Smith if the Trump administration did "have a plan" to respond to the eventual pandemic, Woodward said, "They didn't."
"One of my findings in the book is that President Trump is a one-man band. He decides things. He has his impulses. There are not the kind of serious regular meetings of the National Security Council or the National Economic Council. And being a one-man band, he acts on the impulse of the moment," Woodward added.
Woodward's book is partly based on nearly 20 interviews he conducted with Trump over the course of several months. Last week, it was reported that Trump told Woodward in mid-March that he "wanted to always play it down," referring to the threat of the coronavirus.
"I still like playing it down, because I don't want to create a panic," Trump told Woodward on March 19. On Feb. 28, weeks before that interview with Woodward, Trump had said publicly that the virus would "disappear."
Despite those comments to Woodward, which are on tape, Trump said at an ABC town hall event Tuesday that "in many ways I up-played it in terms of action." White House press secretary Kayleigh McEnany has said Trump "was expressing calm" and "embodied the American spirit" in his pandemic response.
The U.S. now has more than 6.6 million confirmed cases of the coronavirus and at least 195,961 people have died, according to data compiled by Johns Hopkins University. In addition to the significant health toll, the pandemic has caused significant economic damage as states and cities around the U.S. imposed business restrictions intended to slow transmission of the virus.
Millions of Americans lost their jobs, and the stock market also experienced a steep decline, plunging from records highs in late February into bear market territory by late March. That is generally defined as declining 20% or more from recent highs. Wall Street has rapidly recovered since then. The U.S. unemployment rate was 8.4% in August, a marked improvement from its 14.7% coronavirus-era peak in April.
The stock market has recovered tremendously from its pandemic-induced lows, in part due to the fiscal and monetary support unleashed by Congress and the Federal Reserve in hopes of preventing further financial carnage. As of Tuesday's close, the S&P 500 is more than 55% above its March 23 intraday low.
Along the way of Wall Street's swift rally, Trump has touted the robust recovery in equity markets.
Woodward told Smith the stock market is "one indicator of what's going on in the American economy." But, he added, "for the tens of millions of people who don't have jobs, who don't have enough food, who have no steady income, this is a crisis like the Great Depression in terms of people who live here and work here."
Woodward said he asked Trump whether the president was aware of the economic struggle being faced by Americans during the pandemic. Woodward said, "He will acknowledge it. But he's not acting on it."
In August, after key provisions of earlier stimulus expired, Trump signed a series of executive actions he said were designed to provide economic relief to Americans, including a partial extension of the weekly federal unemployment insurance enhancement to state benefits. Trump, who is seeking reelection against Democratic presidential nominee Joe Biden, also initiated action to get the Centers for Disease Control and Prevention to invoke authority to halt evictions for some Americans through the end of the year.
Democratic negotiators in Congress and Trump administration officials remain deadlocked on another broader coronavirus relief package.
"The News with Shepard Smith" premiers at 7 p.m. Sept. 30 on CNBC.