Sen. Lindsey Graham (R-S.C.) said on Sunday morning that he believes the odds are quite good that Senate can pass a narrow measure to avert the "fiscal cliff" and prevent taxes from rising for most Americans.

Graham said on "Fox News Sunday" that the odds are "exceedingly good" a deal can get done. "I don't think people want to go over the cliff," he said. Graham added that such an outcome would be a "political victory" for President Obama.

Graham also said he spoke with Defense Secretary Leon Panetta on Saturday night about the deal, and Panetta said it wasn't likely to address the defense sequester, the automatic reduction in military spending set to take place early next year.

Graham's remarks came as Senate leaders worked through late Saturday to try to strike a deal to extend tax cuts for most Americans. Leaders have set a 3 p.m. Sunday deadline for securing a deal.

Graham cautioned that if a Senate deal does not get 60 percent support from upper chamber Republicans "it will be hard" for House Speaker John Boehner (Ohio) to get it though the House.