Thune: CLASS repeal dead on arrival in the Senate

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"I think we'd get a majority; I don't think we'd get 60," Thune said.

Still, Thune said, the House vote would create "momentum" in the Senate, where Democrats would be put on the spot. Republicans hope to embarrass Democrats by forcing them to support a voluntary payroll tax deduction program that the Obama administration itself has said is unsustainable.

Even getting a simple majority in the Senate would be a tall order. Republicans would need to persuade at least four Democrats to vote for repeal and break party unity, something they've failed to do in the House so far. Only four House Democrats — Reps. Jim Matheson (Utah), Mike Ross (Ark.), John Barrow (Ga.) and Ron Kind (Wis.) — voted for repeal when it came up in committee, and the first three had voted against the reform law in the first place.