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 CruzWarren builds her brand with 2020 down the road Trump wall faces skepticism on border No Congress members along Mexico border support funding Trump's wall 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 LeeTrump should work with Congress to block regulations on prepaid cards Sweeping change at DOJ under Sessions Executive orders alone can't create sustainable deregulatory change 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 RubioTop Trump officials push border wall as government shutdown looms Rubio defends Trump: 'This whole flip-flop thing is a political thing' Rubio: Shutdown would have 'catastrophic impact' on global affairs 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.