House Republicans notified lawmakers that the chamber will vote Monday evening on other bills. They say that will be their only votes of the day.
President Barack Obama and Senate Republican leader Mitch McConnell said Monday they are near a deal to avoid wide-ranging tax increases and spending cuts - the fiscal cliff - that take effect with the new year.
Both men said they were still bargaining over whether - and how - to avoid $109 billion in cuts to defense and domestic programs that take effect on Wednesday.
It remained unclear whether the Senate would vote Monday.
Congress could pass later legislation retroactively blocking the tax hikes and spending cuts.
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