Seniors Mike Elliot and Kevin Berkon organized an impromptu gathering at the statue Tuesday after a plane flew over the campus with a banner that read: "Take the statue down or we will." Berkon said they were "extremely angry" about the message.
"We talked about going up to the statue, and once we got up to the statue, we were like, 'Well, we're going to protect it,'" he said.
Paterno was fired after former assistant coach Jerry Sandusky was charged in November with sex abuse of children on and off campus. Paterno died in January, and Sandusky was convicted of numerous felonies involving 10 boys.
A university investigation recently concluded that Paterno and other top Penn State officials concealed information about the abuse allegations to protect the school's reputation.
University police have an officer monitoring the statue, but Elliot said he and Berkon also want to protect the statue from harm. He said the action isn't intended as a protest.
"We're just simply there to have some numbers around the statue in case anyone wants to come by and vandalize it," Elliot said.
The two students said they would be at the statue again Wednesday night, but weren't sure how long they would keep the vigil. Elliot said police told them they couldn't sleep at the statue, but could keep a tent there.
"That's all right. We'll stay up all night and we'll do what we have to do," he said.
Elliot said he and Berkon "have a lot of respect" for Paterno and support a Paterno family investigation into the incriminating report.
"Seek the truth," he said. "That's what we want to have happen."
Campus police did not return calls seeking comment.