The criticism comes as Donald Trump told reporters in India that the situation is “under control” and that the spread of the disease is a “problem that’s going to go away.”
Mr Romney, a member of the Senate Health, Education, Labor and Pensions Committee, is concerned that the administration has not done enough to prepare for widespread infections.
“I’m very disappointed in the degree to which we’ve prepared for a pandemic, both in terms of protective equipment and in terms of medical devices that would help people once they are infected,” said Mr Romney, The Hill reports.
“At this stage, I think we are substantially underinvesting in what would be appropriate for a setting which could be serious,” he added.
“I think we should be pulling out all the stops,” he said.
Mr Romney is said to be top of President Trump's revenge list after he voted in favour of impeachment in during the Senate trial.
Other members voicing their concerns include Republican Senator John Kennedy of Louisiana, a member of the Senate Appropriations homeland security and health and human services subcommittees.
Mr Kennedy said that the administration, specifically Health and Human Services Secretary Alex Azar, needs to do a better job communicating the level of the threat.
“There’s some real basic questions that the American people need answers [to.] How many cases do we have? Based on their modeling, how many do they think we will have? How’s the virus transmitted?” he said.
“What is the mortality rate? What’s the mortality rate compared to influenza? How many facemasks are we going to need and are we working on getting more? How many respirators are we going to need and are we working on getting more?”.
Mr Kennedy said he wants to know more about concrete steps to stop the spread of the virus in the US and noted that there are conflicting answers on how long it will take to develop a vaccine.
The White House has requested $2.5 billion to prepare the nation for a possible coronavirus outbreak, and Senators have questioned whether that figure is enough.
“If you low ball something like this, you'll pay for it later,” Republican Senator Richard Shelby of Alabama said to secretary Azar. Mr Shelby chairs the Appropriations Committee, which sets spending levels for federal agencies.
Democratic Senator Patty Murray of Washington described the administration's handling of the developing crisis as “unacceptable.”
“We cannot afford to plan on the cheap or at the last minute,” she said, adding that she was deeply concerned.
Senate Minority Leader Chuck Schumer of New York commented: “All of the warning lights are flashing bright red. We are staring down a potential pandemic, and the administration has no plan.”
Azar defended the government's response, stating that two months into the crisis there is no evidence of the virus spreading beyond patients infected overseas and some people that had been in close contact with them.
He said that travel controls and mandatory quarantines were effective and that the government was working on a vaccine and a test to detect the virus.
The government has a stockpile of 30 million N95 respirator masks, but ten times that many are needed for healthcare workers.
At present the US has 57 cases including 40 from the Diamond Princess cruise ship. Globally there are 80,407 cases and there have been 2,708 deaths.
While approximately 95% of cases are in Mainland China, there are rapidly developing hotspots in South Korea, Iran and Italy. The Centres for Disease Control and Prevention today said that Americans should prepare for the virus to disrupt their daily lives.