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 CruzRafael (Ted) Edward CruzDebbie Wasserman Schultz marks 10 years as breast cancer survivor Foreign agent registration is no magical shield against Russian propaganda Let Trump be Trump and he'll sail through 2020 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 LeeMichael (Mike) Shumway LeeSupreme Court takes on same-sex wedding cake case House approves motion to go to tax conference — with drama Trump really will shrink government, starting with national monuments 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 Antonio RubioRyan pledges 'entitlement reform' in 2018 Richard Gere welcomes lawmakers' words of support for Tibet Dem lawmaker gives McConnell's tax reform op-ed a failing grade 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.