A hot beverage maker is provided with a removable pump for cleaning a brewing needle. The pump fits into a brewing chamber which normally receives a pod of an infusible beverage material. A pod receptacle and a lid pivotally connected to the housing form the brewing chamber. After a brewing cycle or when cleaning of the brewing needle is desired, an interior chamber of the pump is filled with cleaning fluid and the pump inserted into the pod receptacle. When the lid is closed, the brewing needle is inserted into the interior chamber. The lid is closed and released repeatedly to operate the pump. This creates a pumping action of the cleaning fluid through the brewing needle to dislodge a buildup of minerals or residual deposits. The used cleaning fluid and dislodged deposits are discarded after the cleaning operation is completed.