The Item reported that Graham was touring his state to warn about the pending cuts, which will start with a $109 billion cut to 2013 spending in January. Like other Republicans, Graham warned that some replacement is needed before then.
"We need to have a sense of urgency about this," he said. "January will be here before we know it."
Senate Republicans have said the Obama administration has not revealed how it would like to structure the sequester, even though officials have said they also oppose the Defense Department cuts. Republicans introduced a bill last week asking for this clarification.
The House has also approved a bill that would replace the required cuts to military and other discretionary spending with deeper cuts to so-called mandatory spending.