Republican South Carolina Sen. Lindsey Graham on Sunday praised President Barack Obama's budget that reportedly cuts future increases to earned benefits programs like Social Security and Medicare.

Several media outlets reported last week that the White House would adopt chained CPI, a less generous way of calculating Social Security cost-of-living increases that assumes seniors will change their buying habits as certain items become more expensive.

Compared with the current model, advocacy group Social Security Works has said that a person who began drawing Social Security at the age of 62 would be receiving 7.32 percent less in benefits per year by the age of 88 under chained CPI.

"I'm looking at the biggest spending cut in American history by reforming entitlements, saving those entitlements," Graham told NBC's David Gregory on Sunday. "And the president's showing a little bit of leg here. This is somewhat encouraging."

"His overall budget is not going to make it, but he has made a step forward in the entitlement reform process that would allow a guy like me to begin to talk about flattening the tax code and generating more revenue."

The senior Republican senator from South Carolina asserted that the key to a grand bargain on the budget was immigration.

"And as to Republicans, the politics of self-deportation are behind us," he warned. "Mitt Romney is a good man. He ran -- in many ways -- a good campaign, but it was an impractical solution. Quite frankly, it was offensive. Every corner of the Republican Party, from libertarians to the RNC, House Republicans and the rank-and-file Republican Party member is now understanding there has to be an earned pathway to citizenship."

Graham added that Obama "showed some leadership" with proposals to cut Social Security and Medicare "and that puts the burden on us to do the same thing."

Watch this video from NBC's Meet the Press, broadcast April 7, 2013.