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Rubio: Defunding ObamaCare more vital than immigration reform

Rubio and a group of Republicans leading the effort have tried to switch the narrative, claiming that it would be Democrats who would be shuttering the government if they didn’t go along with the proposal.

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“The one who's threatening to shut down the government is the president and his Democratic allies,” he said. “What they're basically saying is, unless the budget funds ObamaCare, they won't support it.”

Rubio and the group led by Sen. Mike Lee (R-Utah) have faced resistance from members of their own caucus.

Sen. Tom Coburn (R-Okla.), one of the most vocal critics of the strategy, said on Wednesday the majority of the caucus isn’t behind the proposal.

“We're always open-minded on alternative strategies that would work better,” Rubio said. “But right now there isn't any."