Washington (CNN)Senate Majority Leader Mitch McConnell announced Tuesday he would appoint a bipartisan committee to make recommendations for how to commemorate the memory of Sen. John McCain.
"I am glad we are able to form this gang to ensure that a suitable lasting tribute becomes a reality. I'll have more details to share about this group in the coming days," McConnell said.
Right after McCain's death, Senate Minority Leader Chuck Schumer, a Democrat from New York, announced he wanted to introduce a resolution to rename the Russell Senate office building after McCain, but that was met with a mixed response from Republicans, many of whom said it was too soon to talk about such a major change -- and some outright nixing the idea.
Republican Sen. Bill Cassidy of Louisiana said he would not be in support of renaming the building after McCain -- not out of any disrespect for McCain, but because he doesn't want to create a precedent for renaming institutions that already honor someone's memory.
The building is currently named for Richard Russell, a former senator from Georgia who served for over 40 years.
"This is a question of making sure that however John is honored, it's set in stone that John is always honored," Cassidy said Tuesday. "I don't want to establish a precedent where somebody is unhonored in the future."
Russell, a Democrat, was a segregationist who was opposed the Civil Rights Act. Russell served from 1933 to 1971 and helped write the Southern Manifesto, which outlined congressional opposition to racial desegregation.
McConnell said he would ask a "gang" of lawmakers to meet and talk about the best way to honor McCain but didn't directly address renaming Russell. Instead, he floated renaming the Senate Armed Services Committee room after McCain as well as potentially resurrecting a portrait to the Capitol Senate reception room of McCain.
In a "Dear Colleague" sent to colleagues Tuesday, Schumer and Republican Sen. Jeff Flake seek to drum up support for their resolution to rename the Russell building in McCain's honor, noting the late senator chose offices in the Russell Senate Office Building for the "entire length of service in the Senate."
"Renaming the Russell building in his honor ensures that his story will be told with the hope that inspiration becomes motivation and future leaders merge with his brand of courage and commitment," Schumer and Flake wrote.
Flake, who represented Arizona alongside the Vietnam War veteran, said he's talking to McCain's family in the next couple days to get their feedback on what they prefer regarding a permanent tribute on the Hill.