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Lee and some other Republicans have been leaning on Senate Majority Leader John Thune to launch a talking filibuster to grind down Democrats and advance the measure by a simple majority vote.
He has said he didn’t believe Republicans would hold together to repel a deluge of Democratic amendments that could substantially alter the legislation or target other agenda items important to Trump.
Senate Republicans previously mounted a lengthy floor effort in March to force debate on the SAVE America Act, but momentum behind the legislation has waned considerably in the months since.
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