WASHINGTON (AP) — She imperiled his State of the Union address. He denied her a plane to visit troops abroad.

The shutdown battle between President Donald Trump and House Speaker Nancy Pelosi is playing out as a surreal game of constitutional brinkmanship, with both flexing their political powers from opposite ends of Pennsylvania Avenue as the negotiations to end the monthlong partial government shutdown remain stalled.

In dramatic fashion, Trump issued a letter to Pelosi on Thursday, just before she and other lawmakers were set to depart on the previously undisclosed trip to Afghanistan and...