RELATED: Dr. Fauci Reveals the Key Difference With Vaccinated People Who Get COVID.ae0fcc31ae342fd3a1346ebb1f342fcb During a June 3 episode of CNN’s New Day, Fauci said he is “fairly certain” that the U.S. won’t see a new surge of COVID infections overall following Memorial Day, the way it did after so many holidays over the last year. The country has now administered at least one COVID vaccine dose to more than 50 percent of the total population and has less than 20,000 new daily cases of COVID, per the CDC. But states with low vaccination rates could still see surges. “My concern is, is in those states in which you have relatively few … people vaccinated—when you’re below 50 percent of the people being vaccinated—that’s when you’re going to have a problem,” Fauci told CNN. According to CDC data compiled by Becker’s Hospital Review, more than half of U.S. states should be concerned based on Fauci’s rubric. Only 21 states have given at least once vaccine dose to more than 50 percent of their population. Some states are faring worse than others—like Georgia, Arkansas, Tennessee, Idaho, Wyoming, Alabama, Louisiana, and Mississippi, which have all administered at least one vaccine dose to less than 40 percent of residents. “You may continue to see higher levels of cases as we get into the summer” for these particular states if their vaccination levels remain low, Fauci added. RELATED: For more up-to-date information, sign up for our daily newsletter. For the states that do have a substantial part of their population vaccinated, Fauci says there is very little concern about post-holiday spikes. “If you have a very high percentage of people vaccinated, you’re not going to see a substantial blip—you may see a little bit, not anything that even resembles a surge,” he noted. This doesn’t mean the country should get complacent, especially now that vaccination rates are slowing down and most states aren’t anywhere near fully vaccinated. “The one thing we want to make sure is that we don’t declare victory prematurely and feel that because things are going in the right direction that we don’t have to keep vaccinating people,” Fauci said. “We’re on a really good track now to really crush this outbreak. And the more people we get vaccinated, the more assuredness that we’re going to have that we’re going to be able to do that.” RELATED: Dr. Fauci Thinks These 3 Places Will Mandate Vaccines.