She added the caveat that "900 specific weapons" ..."will not fall under the bill."
President Barack Obama, she believes, will support the legislation.
Back in Washington, Murray is weary but optimistic.
"Look at those beautiful babies," the mother said, her voice shaking. "Look at those children at Sandy Hook. I just want to tell people in Washington to do what is right."
She's exhausted. So is her daughter Tess.
The teenager's school was in lockdown on Friday. When she got home later in the day, all she could do was hug her parents.
She casually says, "The next time my school is on lockdown," perhaps not realizing that she thinks there will be another time, no matter the circumstances, when a school is afraid.
"I trust the teachers in my school and the faculty, especially after seeing how they reacted," she said. "But I'm worried that everyone is going to be terrified.
"I know kids around the world feel the same way. They are going to know that this could happen to them. I just want to be a part of trying to change that."