Senator Maria Cantwell, Democrat of Washington State and chairwoman of the Indian Affairs Committee, said in an interview on Sunday that lawmakers would “definitely” examine the N.F.L.’s tax-exempt status and other ways to pressure the league.

“You’re getting a tax break for educational purposes, but you’re still embracing a name that people see as a slur and encouraging it,” Ms. Cantwell said.

In a copy of the letter released on Sunday, Ms. Cantwell and Representative Tom Cole, Republican of Oklahoma and a member of the Native American Caucus, chided the N.F.L. commissioner, Roger Goodell, for his recent remark that the name of the team, based near Washington, D.C., “honored” Native Americans.

“The N.F.L. can no longer ignore this and perpetuate the use of this name as anything but what it is: a racial slur,” they said.