Her “new Brexit deal,” as she described it, would give Parliament a broader role in shaping her plan. But the part that drew the most attention was her vague offer to have lawmakers vote on whether to have a second referendum, something she had previously ruled out. It was unclear what questions any referendum would pose.

The plan seemed designed to entice pro-Brexit Labour Party lawmakers to support her Brexit blueprint.

Key issues: Her plan includes the opportunity for Parliament to decide whether to keep a type of customs union with Brussels, eliminating tariffs and reducing checks on goods at frontiers. Another issue is the Irish border, and the deal would commit the government to working on measures to track goods.

Response: The Labour leader, Jeremy Corbyn, said his party would not support the plan. Pro-Brexit Conservatives have also reacted angrily.

Reminder: Mrs. May essentially promised to step down no matter what lawmakers decide about her plan. The vote on Brexit legislation is set for the week beginning June 3.