Schumer and Flake are privately sending a "dear colleague" letter to every senator urging them to sign on as co-sponsors to their forthcoming resolution, which would rename the Russell Senate Office Building after the late GOP senator.

"Renaming the Russell building in his honor ensures that his story will be told with the hope that inspiration becomes motivation and future leaders emerge with his brand of courage and commitment," Schumer and Flake write to their colleagues in the letter.

They added their "strong belief is that future generations should know the story of Senator John McCain."

The Russell Senate Office Building is where McCain's office and the Armed Services Committee, which McCain oversaw, is located.

The letter aimed at building support for renaming the building comes as some GOP senators are pushing back against the idea.

Russell, a Democratic senator from Georgia, is considered controversial because of his opposition to civil rights legislation. But asked about that on Tuesday, Shelby noted that he was a "man of his time."

"If you want to get into that you have to get into George Washington and Thomas Jefferson and all of our — most of our Founding Fathers, maybe with the exception of Hamilton," he added. "It's easy to prejudge what they should have done."

"I'm going to follow the leadership on this," he said. "I mean that's a big decision on what to do. I want to appropriately honor Sen. McCain and I'll vote for almost anything that will do that."