Connecticut Gov. Ned Lamont told CNBC on Tuesday he's concerned that the number of ventilators in the state wouldn't be enough to handle a dramatic surge in coronavirus cases.

"We have a long way to go there," Lamont said in a "Squawk Box" interview. "We do have some capacity there at this point, but I am worried. If we cannot flatten that curve, as they say, we could be overwhelmed."

Lamont said that is why social-distancing efforts are so critical. He said they are necessary to ensure a flattening of the curve — essentially trying to limit the surge of coronavirus cases.

Lamont on Monday announced a joint agreement with fellow Democratic governors of New York and New Jersey to limit density throughout the region, prohibiting crowds of 50 or more and closing restaurants and bars except for takeout and carryout orders.

The U.S. has more than 4,600 confirmed cases and 85 deaths, according to Johns Hopkins University data.

Lamont declared a state of emergency a week ago, when Connecticut had four confirmed cases. As of Tuesday morning, the state had 41 confirmed cases and no deaths.

The governor said he was less worried about the number of hospital beds in Connecticut, saying the state could get creative to add capacity.

"I think we could commandeer a lot of beds. We have our universities down right now. We have hotels that aren't fully occupied, so that's a little less urgent to me in terms of my priorities," he said.

It gets more difficult to add ventilator capacity, he said, adding he's not counting on the federal government to supply the state with an appropriate amount.

"You don't just go to Amazon to get a ventilator," Lamont said. "I was on the phone for hours yesterday with hospitals, saying, 'This may be on us and we've got to take the lead on this. Where do you source this? What can I do to help?'"

During a video conference Monday, President Donald Trump reportedly told a group of governors they may have to obtain their own medical equipment that's in short supply as the nation faces an explosion of respiratory infections with the pandemic.

"Respirators, ventilators, all of the equipment – try getting it yourselves," Trump told the governors, The New York Times reported, citing a recording of the conference call.