Hillary would have botched this horribly, just like she did Benghazi.
I have no idea how Hillary would have handled this. But probably the CDC teams in place when Obama left would still be in place operating effectively, the CDC Chinese-speaking expert working with Chinese virologists in Beijing would have been there getting the inside dope and passing it on, and the intelligence agency reports conflicting with what Trump was hearing from Xi would have gotten a much greater hearing. I despised Hillary, and I am not generally a fan of our intelligence agencies, but such are the facts...
Hillary's presidency would have just been a continuation of Obama's policies. During the 2009 outbreak of H1N1, Obama didn't even declare a national emergency until the death toll went way up. Let's look at how President Trump has handled this:
The first confirmed case of coronavirus in the United States was announced on January 21, 2020.
On January 31, 2020, President Trump ordered all Americans returning home after traveling in China’s Hubei Province to submit to a 14-day quarantine.
On Feb 3, 2020, President Trump orders a travel ban to China. Democrat Senate Minority Leader Chuck Schumer declares oversight is needed since President Trump is "overreacting."
Now let's compare it to President Obama's reaction to the H1N1 Swine Fly epidemic of 2009:
Spring 2009
– The H1N1 flu pandemic in the United States commonly referred to as “swine flu”, had spread into the US from an outbreak in Mexico.
April 2009
The CDC identified the first two H1N1 / Swine flu cases in California on April 17, 2009. On April 28, 2009, the director of the Centers for Disease Control and Prevention confirmed a 23-month-old toddler in Texas became the first official U.S. death of H1N1 / Swine flu.
May 2009
The H1N1 Virus had infected American citizens in all 50 states.
June 2009 – Two Months After The First U.S. H1N1 was confirmed:
There were a total number of 27,717 confirmed cases of H1N1. Toward the end of June, the number of deaths related to the virus in the US surpassed those of all other countries.
On June 25, the CDC released information revealing that there were more than likely over one million (1,000,000) cases of the disease in the US, most of which had not been reported or diagnosed.
As of March 9, 2020, there were 582 confirmed coronavirus cases in the U.S. (compared to Obama’s 27,717)
22 Americans Had Died of Coronavirus (compared to Obama’s approx. 1,000)
Coronavirus has been confirmed in 34 out of the 50 U.S. states (Compared to Obama’s handling that saw H1N1 in all 50 states within the first month)
Finally, SIX-MONTHS AFTER H1N1 had spread to all 50 States, on October 24, 2009, President Barack Obama declared a national emergency in the United States.
When President Barack Obama declared a national emergency on October 24, 2009, the CDC estimated that 4,000 Americans have died. 22 million Americans had been infected with the H1N1 virus.
Dec. 2009
Just 16 days later on December 10, 2009, the CDC reported that 50 million Americans or 1 in 6 people had been infected with the 2009 A H1N1 Virus. 6,000 additional Americans had died, bringing the total to 10,000. The H1N1 vaccine was just beginning to be widely distributed to the general public by several states.
Jan. 2010
On January 15, 2010, the CDC released new estimate figures for the H1N1 / Swine flu. 55 million Americans had been infected, and 11,160 Americans had died between April through mid-December, 2009.
March 2010
By mid-March 2010, the U.S. Centers for Disease Control and Prevention estimated that 59 million Americans contracted the H1N1 Virus, 265,000 Americans were hospitalized, and 12,000 Americans had died.
Hillary would have not handled this any better than Obama, nor would she have handles it any better than President Trump has.