Graham backs House ObamaCare bill, though he criticized strategy

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 CruzThis week: Shutdown deadline looms over Congress Five things to watch for at Trump-Clinton debate Week ahead: Funding fight dominates Congress 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 accepts Cruz endorsement after saying he wouldn't In reversal, Cruz endorses Trump The Hill's 12:30 Report 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 RubioSenate rivals gear up for debates Rubio: End of Obama's term could be 'most damaging yet' Fifteen years since pivotal executive order, STORM Act could help fight terror finance 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.