"He’s got a certain talent for this," Trump said at Wednesday's White House briefing as he sought to reassure the public on how the White House is dealing with the virus, which has infected at least 60 Americans so far.
Others, however, have criticized Pence's response to the state's worst outbreak of HIV in its history and the nation's first HIV outbreak linked to the injection of oral painkillers while he was Indiana's governor in 2015. The crisis began when people started injecting a liquid form of a potent painkiller multiple times a day and sharing needles.
While health officials advocated for a clean-needle exchange to slow the spread of infection, Pence staunchly opposed the program on grounds it could encourage or support drug abuse.
"I don’t believe effective anti-drug policy involves handing out drug paraphernalia," Pence said at the time. "I don't believe that effective anti-drug policy involves handing out paraphernalia to drug users by government officials."
It wasn't until two months after the outbreak was detected -- and at least 75 people were confirmed HIV-positive -- that Pence declared a state of emergency. He announced he'd allow a needle exchange program for 30 days but added that if the legislature sent him a broader needle exchange program bill, he would veto it.
The outbreak highlighted the weaknesses in Indiana's health infrastructure as it placed 41st nationally in America's health rankings.
Studies in medical journals have said the epidemic could have been prevented if the state had acted faster.
After conducting a 2018 Yale University study on the outbreak, researcher and associate professor, Forrest W. Crawford, said: "Our findings suggest that with earlier action the actual number of infections recorded in Scott County -- 215 -- might have been brought down to fewer than 56, if the state had acted in 2013, or to fewer than 10 infections, if they had responded to the [hepatitis C] outbreak in 2010-2011."
"Instead they cut funding for the last HIV testing provider in the county," Crawford added.
Since a Planned Parenthood clinic in the Scott County -- where the outbreak originated -- had closed in 2013, free HIV testing wasn't available in the area. Pence, as a member of Congress, voted to cut Planned Parenthood funding in 2011.
While there is no direct link between the closure and the outbreak, had a center provided HIV tests in Scott County, workers could have reported positive results to the state.
But Dr. Jerome Adams, Pence’s health commissioner at the time who now serves as U.S. Surgeon General, defended the governor, saying he needed certainty that he was doing the right thing.
"The governor wanted to make sure if we went this route it was absolutely necessary," Dr. Adams said at the time. "I believe he was praying on it up until the final decision."
Critics, however, say that Pence's track record does not qualify him to lead a national health crisis.
House Speaker Nancy Pelosi said Thursday morning on Capitol Hill that she spoke with the vice president and expressed her concerns of him holding the position.
"While I look forward to working with him," she said, "while he was governor of Indiana, slashing the public health budget and having some clinics, especially a Planned Parenthood close, which was the only place in that Scott County where you could get tested for HIV and AIDS. There was an outbreak. Again, he will have his side of the story."
"This is about resources. It's also personnel. It's also about respect for science and evidence-based decision making," she added.
Democratic presidential candidate Bernie Sanders, I-Vt., took to Twitter Wednesday evening, calling Trump's plan to have Pence lead the response "disgusting," adding that Pence "wanted to 'pray away' HIV epidemic."
Leana Wen, the past head of Planned Parenthood, also tweeted Wednesday: "As Governor of Indiana, an HIV/AIDS epidemic flourished until he allowed public health -- not ideology -- to direct policy & response."
A different researcher on the 2018 Yale University study said in a tweet that Pence's slow response "fueled an HIV outbreak in his state." Noting that Pence is not a doctor or scientist, Trump "made the choice of putting someone absolutely not up to the task to this crucial position. It endangers us all. This isn't a Republican or Democratic issue," Greg Gonsalves tweeted.
It's not the only public health issue on which Pence is facing criticism.
As late as 2000, Pence also downplayed the risk of smoking, as evident by an op-ed, unearthed by Vox, on his congressional website: "Despite the hysteria from the political class and the media, smoking doesn’t kill."
At Wednesday's briefing, Trump emphasized that Pence would not be a coronavirus "czar" as "he is a part of the administration," but he is expected to be the face of the response.
While some have speculated that the move to appoint Pence is a blow to Health and Human Services Secretary Alex Azar, Azar called the move "genius" in a hearing on Capitol Hill on Thursday.
As he testified at a House Ways and Means Committee hearing Thursday, Azar was asked by Rep. Jimmy Panetta, D-Calif., if the coronavirus task force will follow the advice of medical experts, citing what he called Pence's "slow walk" in responding to the 2015 HIV outbreak in his state.
"As you know, one of the largest outbreaks of another virus, HIV, occurred in Indiana. It was the result of critical testing sites and clinics being closed due to cuts to state funding. When it was determined that the cases were spiking due to needle sharing, then Governor Pence failed to heed the advice of medical experts. He really did slow walk the needed public health response," Panetta said. "Can you assure us, Mr. Secretary, that HHS will follow the advice of leading medical experts and not delay implementation?"
"I always follow the advice of my career officials in these matters," Azar replied. "I trust them completely."
ABC News' Stephanie Ebbs contributed to this report.