They leapt to their feet, dozens of Democratic women, jubilant in their hues of suffragist white as they hugged and grasped hands. For most of the night, they had frequently been stone-faced, often reluctant to applaud President Trump’s declarations.

But at his acknowledgment of their own accomplishment in his Tuesday night State of the Union address — a record number of women elected to Congress — they broke out into beaming smiles matching Mr. Trump’s, waving and joining in a “U.S.A.” chant across the House chamber.

It was a culmination of emotion after a long day of preparation and anticipation for one of the capital’s most elaborate rituals. After a cancellation of the speech and weeks of posturing amid a government shutdown, and with another potential funding lapse looming, it was finally time to hear what, exactly, the state of the union was.