Sen. Lindsey O. Graham (R-S.C.) gave President Obama some advice Monday on how to forge a deal over the national debt. 

Graham said in an interview on Fox News that Republicans were not planning to budge on refusing to raise the debt ceiling without spending cuts, and he accused Obama of playing "small ball" by urging a tax-rate hike on top earners. 

Obama said last week he will not let Republicans use the threat of withholding a debt ceiling increase to force spending cuts. Federal borrowing authority runs out around February. Graham said Republicans would not give up on using the debt ceiling as a bargaining chip.  

"You just got reelected. How about doing something big that is not liberal?" Graham said, around 3:22 in the video above. "How about doing something big that really is bipartisan? Every big idea he has is a liberal idea that drowns us in debt. How about manning up here, Mr. President, and use your mandate to bring this country together to stop us from becoming Greece?"  

Graham said the "big solution" would involve reforming entitlements. Letting tax cuts expire, he argued, would not raise enough revenue. 

"I would like [Obama] to be remembered for a president who saved Social Security and Medicare from bankruptcy by working with Republicans," Graham said. "But he seems to have no inclination to be remembered for anything other than a guy who has a small view of our fiscal situation." 

Graham's claim in previous interviews that Medicare, Medicaid and Social Security are all headed for bankruptcy was debunked by the Fact Checker

A growing chorus of Republicans is pushing for a deal that exchanges tax rate increases for entitlement reform. Obama has proposed $350 billion in health savings over the next decade. House Speaker John A. Boehner (R-Ohio) has suggested $600 billion from health programs and an additional $200 billion from using a stingier measure of inflation, reducing cost-of-living increases for Social Security recipients.