He was also dismissive of the resolution’s prospects for success, telling Talking Points Memo that he “[didn’t] see [Obama] agreeing to defund his signature issue.”

Back in July, Graham had referred to defunding ObamaCare as "a bridge too far" for him.

A spokesman for Graham said that the senator had always supported defunding ObamaCare, but simply rejected a strategy that involved shutting down the government. He also said Graham was rejecting the strategy, advocated by Senator Ted CruzTed CruzPaul: Pence should oversee Senate ObamaCare repeal votes Senators introduce new Iran sanctions With no emerging leaders, no clear message, Democrats flounder MORE (R-Texas), that Senate Republicans immediately filibuster the House resolution in the Senate to prevent Democrats from invoking cloture and then re-adding funding for ObamaCare via a majority vote.

Conservative backers of the plan to defund ObamaCare such as Sen. Mike LeeMike LeeOvernight Finance: Senators spar over Wall Street at SEC pick's hearing | New CBO score for ObamaCare bill | Agency signs off on Trump DC hotel lease GOP senators offer bill to require spending cuts with debt-limit hikes Healthcare fight pits Trump against Club for Growth MORE (R-Utah) have denied any intent to trigger a government shutdown, saying the only people willing to shut the government down are Democrats who refuse to back a spending resolution unless it funds ObamaCare. Lee, Cruz, and Marco RubioMarco RubioSenators introduce new Iran sanctions Senate intel panel has not seen Nunes surveillance documents: lawmakers With no emerging leaders, no clear message, Democrats flounder MORE (R-Fla.), the leading proponents of the defunding effort, all endorsed the House's resolution.

Graham is currently facing multiple primary challengers who accuse the senator of being too centrist. In late August, several Tea Party groups began a series of online ads attacking him for not committing to the defunding effort.