Who is in charge of the U.S. now? Why?

From the text:

The next voice you hear will be that of the Acting Chief Executive of the United States, Mrs. Josephine Vanbruuker-Brown-"

Ms. Brown is in charge because the President has been killed, and it is presumed that Washington has been destroyed.

These first sentences had been clearly and bravely spoken. Now her voice faltered, as if she found it difficult to say what it was now necessary to say. "The very fact that I speak to you as the Chief Executive of the nation must tell you much."

They heard her sob. "No President," Helen whispered.

"No Washington," Randy said. "I guess she was out of Washington, at home, or speaking somewhere, and wherever she lives-"