Nevada Democratic Sen. Jacky Rosen told "CBS Mornings" on Thursday that while it is not uncommon for her office to receive calls from people disagreeing with her and her staff, the threatening and antisemitic messages that targeted her last month were upsetting.

"And it didn't hit me until my daughter saw it," Rosen said. "And when she called me crying, thinking that something was going to happen to me, that someone threatened my life, I saw it not as a senator, but as a mother. And that is when it really hit home to me, that something bad could happen."

Rosen, who is Jewish, said her daughter is about to turn 28. 

"So she's a grown woman, but it doesn't matter," Rosen said. "She understands, but I don't care how old you are. Your mom is still your mom. You could be 80 and your mom a hundred. It's still your mother, the person you love most."

Nevada police arrested John Anthony Miller, a 43-year-old Las Vegas resident, for allegedly leaving menacing messages on the office voicemail of a U.S. senator and traveling to a federal courthouse in Las Vegas where the senator has an office, according to court records unsealed Monday. While court documents did not identify the targeted lawmaker, a spokesperson for Rosen confirmed earlier this week the messages were left with her office.

Miller is accused of calling the senator "vermin" and threatening to "finish what Hitler started." He is charged with one count of threatening a federal official. His attorney, public defender Benjamin Nemec, declined to comment on the charge when contacted earlier this week by CBS News.

The alleged threats came amid a broader increase in antisemitic incidents nationwide following the Oct. 7 attacks by Hamas in Israel, and Israel's response in Gaza, which Hamas governs. More than 300 antisemitic incidents occurred between Oct. 7 and Oct. 23, up from 64 in the same time period last year, according to a recent report by the Anti-Defamation League, a nonprofit organization that tracks such threats. The spike included a 388% increase in incidents of harassment, vandalism and/or assault compared to that same time period in 2022.

In one case, an engineering student at Cornell University in New York was arrested Tuesday on federal charges that he made violent antisemitic online threats against Jewish students at the school. 

Rosen said students on college campuses are worried, and that universities have a responsibility to keep them safe.

Robert Legare contributed to this report.