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The other Republicans joining Mr. Camp in sponsoring the bill were Reps. John Kline of Minnesota, the House Ways and Means Committee chairman; Steve Scalise of Louisiana, the Republican Study Committee head; and Steve Southerland II of Florida.

“The president may think his work waiver helps Americans in need, but, in reality, all he’s done is rob them of their dignity and made it harder for them to lift themselves out of poverty,” Mr. Southerland said.