Sen. Dianne Feinstein, D-California, said it would be a "huge mistake" for the NFL to allow its players to continue to play if they are convicted of violent felonies.
"What's happened is a dramatic growth in violence and I think if you combine violence with alcohol in a social setting you get a very unpredictable result. I think there is no place for this, period," Feinstein said on CBS' "Face the Nation" Sunday.
The California senator's comments were prompted by a question about the decision to keep San Francisco 49ers defensive end Ray McDonald in the starting lineup even though he was arrested on suspicion of domestic violence in August. He has not been charged.
"I believe very strongly that if a player is arrested they should be suspended," said Feinstein, who was the mayor of San Francisco in the late 1970s and 1980s. "This has gone on too long, it is getting too bad and this team, these teams have to set an example for the rest of society.
"Football is a major sport. The NFL is a great league....but there has to be a strength in the league and they have to project the values of what's right and what's wrong, and to let players continue to play after they've been convicted of what would be a felony, I think is a huge mistake," Feinstein said.
She was one of 16 female senators who sent a letter to NFL Commissioner Roger Goodell earlier this month saying the league needs a "zero-tolerance" policy for players who commit acts of violence against women.
CBS News special correspondent James Brown, the anchor of NFL Today, said in a separate interview on "Face the Nation" said that the NFL needs to create a policy for domestic violence issues.
"A policy needs to come from the top down and not leave the individual 32 teams with determining what that should be," Brown said. "I think there is consensus that if a player is accused of domestic violence then until the facts are in that player ought to be sat down with pay. If in fact the player is convicted of the charge then they ought to face some type of stiff penalty, whatever that is, six games, a year, without pay. It's as simple as that. "
He added that many people think Goodell should give more specifics about the issue.
Additionally, he said, "Quite frankly, a number of players want to see that the commissioner be subjected to some type of fine and/or suspension because that's exactly the kind of standard that he's held the players to."
Goodell has come under fire for how he handled the case of Ray Rice, the former Baltimore Ravens running back who was seen in recently-released videos punching his then-fiancee in an elevator.
An ESPN report published over the weekend indicated that the Ravens knew about the video long before it became public and sought a lighter punishment for Rice, and that the team's owner, Steve Bisciotti, sent Rice a text message offering him a job with the team once he retired from football.
"With respect to the text messages specifically that the report talked about, I asked Steve Bisciotti about that. He acknowledged and was very forthright that he had sent two text messages to Ray," Brown said.
"In terms of whether people wanna see that as him trying to buy Ray Rice's silence, I don't necessarily see it that way. I thought that Mr. Bisciotti was very forthcoming in what he had been offering to Ray in terms of support of the organization and potentially a job afterwards which is not different than what he's done with the previous player, Dante Stallworth was an ex-NFL player who unfortunately was inebriated and involved in a car accident that killed an innocent person as well," said Brown.
Face the Nation Anchor Bob Schieffer incorrectly said that Ray McDonald has been charged with felony assault on his wife. McDonald was arrested, but has not been charged, and the incident involved his fiancee.