A measure to direct the president to halt U.S. engagement in Iran had been on track to pass in late May, but Republican leaders postponed action. They have run out of time to delay the vote.
The president's pick for governor of Iowa lost his primary, while Democrats in the state chose their nominee in what they hope will be a competitive Senate race.
Mr. Pelley, a longtime correspondent and former "Evening News" anchor, harshly criticized the show's leadership in an extraordinary exchange during a staff meeting on Monday.
President Trump has argued that the United States is "stupid" for granting citizenship at birth. Most countries don't do so, but that can create problems.
In an explosive staff meeting, Mr. Pelley, a correspondent for the long-running Sunday news show, blasted Bari Weiss, the CBS editor in chief, and Nick Bilton, the show's new executive producer.