This week, Graham and fellow Republican Rand Paul of Kentucky will bring forth a plan to overhaul the 75-year-old social safety net.
"We're going to have a Social Security Solvency bill that deals with age adjustments and means testing" Graham says.
In other words: we're talking about working longer, retiring later; and reducing benefits for well-off Americans. For their part, Democrats -- including Sherrod Brown of Ohio --have already begun to circle the wagons.
"We want to make sure what doesn't happen - and what doesn't happen is a privatization of social security or a cutting of benefits," he says.
Nor is this senator from a rust-belt state down with the idea of upping the retirement age.
"There are an awful lot of Ohioans, an awful lot of Americans who are on a shop floor all day or work in construction or work in a diner. Their bodies don't work until they're 70 in most cases. So raising the retirement age, reducing benefits, is just off the table as far as I'm concerned," Brown says.
The mere facts of longer life-expectancy and an aging baby-boom generation make for inevitable questions about the long-term financial stability of the program. Social Security has long been known as a dreaded "third rail" in American electoral politics -- as in, touch it and you can kiss your sweet office goodbye. Graham seems to think times have changed.
"I think the third rail now for American political leaders is to not do the things that need to be done to save America from financial ruin," he says.
As of now, Graham's approach doesn't have the votes in the Senate. His would-be co-reformer, Paul, is undeterred.
"There are votes you win and there are votes you put out there to try to show what we would do if we had a majority," he says.