Washington (CNN) - Republican Sen. Lisa Murkowski told CNN on Tuesday she is "concerned" that the most recent charge of sexual harassment against Republican presidential candidate Herman Cain "is not an isolated incident" and that he should quit the race if there is any truth to the claims.
"I'm learning about this at the same time as any of the rest of you. But I would suggest that if, in fact, there is substance to the claims - and now there are apparently four individuals that have been involved or who have come forward - if that's the case, I think that his opportunity as a nominee are gone," the senator said.
Nearly all of the Republican senators contacted by CNN sidestepped questions about the scandal that has rocked Cain's campaign, saying they want to learn first if there is real evidence to support the mostly anonymous charges.
However, Murkowski made clear she was moved by the public account of Sharon Bialek, a single mother from Chicago who held a news conference on Monday to say Cain wanted sex in return for helping her to find a job.
"It takes incredible courage for an individual to come forward as this latest, as this one woman has," the third-term Alaskan said. "So it does cause me to wonder exactly what is out there. I am concerned."
Cain is scheduled to hold a news conference later Tuesday to address the claims.
Murkowski acknowledged that it's possible the claims against Cain are "spurious" and said it's important "that we get to the bottom of it and make a determination."
Asked if Cain should quit the race if he had done anything like this, Murkowski responded without hesitation.
"Yes," she said.