"It's about time to assume the worst," Graham said on CNN's State of the Union on Sunday.
Graham added that ISIS is no longer a minor or amateur terrorist organization.
"They're not the JV team anymore," Graham said. "They're the most prominent terrorist organization in the world but they're not the only one. They're in competition with the other terrorist groups and the gold medal will be awarded to the one that can hit America."
Graham continued that the threat posed by the group, which has prompted the United States to conduct a series of airstrikes in Iraq against the militants, should receive a proportionate response from the United States.
"We should, in my view, look at ISIL as a direct threat to the United States, a direct threat to the region that cannot be accommodated," Graham said. "We are now directly threatened by ISIL." Graham added that the response to ISIL should be proportionate to the threat the group has been posing.
Graham said the U.S.'s "strategy and manpower" should meet that threat.
Graham's comments come a few days after Army General Martin Dempsey, the chairman of the Joint Chiefs of Staff, described that the Islamic State Group as having an "apocalyptic, end-of-days strategic vision" in the Middle East and can only be defeated if the United States and a group of partners face it directly in Syria.