In one letter, 49 senators cited the NBA's quick action recently to ban Los Angeles Clippers owner Donald Sterling for life after he was heard on an audio recording making offensive comments about blacks. They said Goodell should formally push to rename the Redskins.
"We urge you and the National Football League to send the same clear message as the NBA did: that racism and bigotry have no place in professional sports," read the letter, which did not use the word "Redskins."
The letter comes at a time of growing pressure to change the team name, with statements in recent months from President Barack Obama, lawmakers of both parties and civil rights groups.
Sen. Bill Nelson, a Florida Democrat, wrote his own letter saying he doesn't believe that retaining the Redskin name "is appropriate in this day and age." He described himself as "one of your great fans for both the game and you personally."
Redskins owner Daniel Snyder has refused to change the name, citing tradition. The franchise has been known as the Redskins since 1933, when it played in Boston.
In a written response, NFL spokesman Brian McCarthy said "diversity and inclusion" has long been a focus of the NFL.
"The intent of the team's name has always been to present a strong, positive and respectful image," McCarthy said. "The name is not used by the team or the NFL in any other context, though we respect those that view it differently."
Senate Majority Leader Harry Reid, D-Nev., and Sen. Maria Cantwell, D-Wash., led the letter-writing effort. All senators on the letter are Democrats. Cantwell spokesman Jared Leopold said Republicans were not asked to participate.
Democrats not signing the letter were Tim Kaine and Mark Warner of nearby Virginia, where the team's headquarters are; Mark Pryor of Arkansas, in a tight re-election race this year; and Joe Manchin of West Virginia and Joe Donnelly of Indiana, two of their party's more moderate lawmakers.
The senators noted that tribal organizations representing more than 2 million Native Americans across the U.S. have said they want the Redskins name dropped.
Despite federal laws protecting their identity, "Every Sunday during football season, the Washington, D.C., football team mocks their culture," they wrote.
"The NFL can no longer ignore this and perpetuate the use of this name as anything but what it is: a racial slur," the letter said.
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