Which of the following statements is true of the president's veto power? If the president signs a bill within ten congressional working days after the bill is submitted, it results in a pocket veto. Congress can override a veto by the president only if there is a unanimous vote by the members present in each chamber. If the president does not send a bill back to Congress after ten congressional working days, the bill becomes law without the president's signature. The result of a veto override by Congress is that the bill cannot become law against the wishes of the president.