But sounding vexed during the show, Graham seemed not only chafed by the Senate voting down a Republican effort to amend the preamble of the treaty; he also linked the START treaty to his resentment over how the current lame-duck session of Congress has turned out.
Graham exclaimed how hard it was to pass a bipartisan compromise over extending the Bush era tax cuts, and expressed his disappointment over repeal of the military's "Don't Ask, Don't Tell" policy banning openly gay service members.
"If you want to have a chance of passing START, you better start over and do it in the next Congress, because this lame duck has been poisoned," Graham told CBS News chief Washington correspondent Bob Schieffer.
"The last two weeks have been an absolutely excruciating exercise. 'Don't Ask, Don't Tell,' a controversial topic - some say the civil rights issue of our generation, others say battlefield effectiveness - was passed in the lame-duck session without one amendment being offered," Graham said.