"This deficit reduction package is grotesquely unfair, and it is also bad economic policy," he said.
McConnell faced some opposition from his right flank.
But despite dissatisfaction, conservative Senators, including Jim DeMint (R-S.C.), Rand Paul (R-Ky.) and Mike Lee (R-Utah), said they would not block the Senate from voting on the bill.
Paul and Lee, however, said they wanted time to read and understand the bill — even though they are almost certain to oppose it.
Jessica Brady, Meredith Shiner and Steven T. Dennis contributed to this report.
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