WASHINGTON—Key Senate Republicans on Wednesday brushed aside fresh warnings from U.S. Treasury Secretary Timothy Geithner that Congress must increase the U.S. borrowing cap before an Aug. 2 deadline.

Mr. Geithner, in two letters to lawmakers, shot down Republican claims that the U.S. can continue to meet its debt obligations after Aug. 2 even if a debt ceiling deal isn't reached. He also criticized a Republican proposal for the government to develop a contingency budget plan that could be used if the debt cap isn't raised.

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