When Senate Minority Leader Charles E. Schumer (D-N.Y.) called for renaming the Russell Senate Office Building after John McCain, it was widely seen as a fitting testament to the late Republican senator’s legacy and his bipartisan approach during more than three decades in Congress.

Yet days after his death, some Senate Republicans are already wary of the idea, with some Southerners citing the legacy of Sen. Richard Russell Jr., a master of the Senate with a list of accomplishments but also a segregationist who led Southern opposition to civil rights. Russell was a Democratic senator for 38 years until his death in 1971.

The Georgia lawmaker’s controversial racial legacy has led to calls to rename the 110-year-old building in the past, but they fizzled because of a lack of enthusiasm on both sides of the aisle.

Senate Majority Leader Mitch McConnell (R-Ky.) told reporters on Tuesday that he had not been notified in advance of the plan by Schumer.

McConnell instead recommended creating a task force to study ways to commemorate McCain with the goal of “proper recognition in a calmer environment.”

One possibility, McConnell said, includes the addition of the late senator’s portrait to the Senate Reception room — considered a “hall of fame” for the most distinguished senators who have served.

The room, located next to the Senate chamber, is currently adorned with artwork depicting fewer than a dozen senators, including Henry Clay, Daniel Webster, John C. Calhoun and Robert A. Taft, Sr.. A special committee chaired by Senator John F. Kennedy (D-Mass.) chose the first portraits to hang in the room in 1957.

“The Senate is eager to work on concrete ways to .... provide a lasting tribute to this American hero long after this week’s observances are complete,” McConnell said in remarks on the Senate floor.

His caution was matched by fellow Republican senators, who cast doubt on Schumer’s proposal and said they favored commemorating McCain in some way but not necessarily by renaming the Russell Building after him.

Such warnings served as a reminder of McCain’s testy relationship with the Republican Party establishment, from which he diverged on issues including torture, taxes and health care, alongside his outspoken opposition to President Trump.

“We’ve honored John McCain, but Richard Russell was an icon,” said Senate Appropriations Committee Chairman Richard C. Shelby (R-Ala.). “I didn’t serve with him, but he was an icon in his day.”

On Russell’s support for segregation, which included co-authoring the Southern Manifesto with Strom Thurmond in 1956, Shelby said, “You go back to George Washington, Thomas Jefferson, just about anyone, nobody’s perfect.”

Judiciary Committee Chairman Sen. Charles E. Grassley (R-Iowa) said, “I think I’d be in favor of naming almost any building for McCain, but I’m not sure that I want to make a decision on a specific building at this point.”

“I certainly look forward to doing what is best and what his family wants. I haven’t had the chance to talk to his family about it,” said Sen. Cory Gardner (R-Colo.).

Renaming the Russell Building would fall within the jurisdiction of the Senate alone, unlike other federal properties where the president’s signature is required. The proposal would likely fall to the Senate Rules Committee before going to a vote.

The chairman of that committee, Roy Blunt (R-Mo.), told reporters: “I am open to that. I think we ought to have a little discussion about changing the name of a building, but certainly John McCain should be recognized in some way.”

He emphasized that McCain “always wanted to get things done in a regular order.”

He was among several GOP senators to warn that procedures needed to be followed.

“I think we should mirror the process we’ve gone through in the past,” said Sen. Roger Wicker (R-Miss.). “I think the majority leader has the right idea in giving a process.”

Sen. Lindsey Graham (R-S.C.), one of McCain’s closest friends on Capitol Hill, quipped that he would “like to name the Pentagon after him just to get back at everybody.”

Graham sounded a cautious note about renaming the Russell Building, however.

“I don’t know what the right way to honor John is. In terms of naming stuff, here’s what I hope we’ll do, instead of worrying what we’ll name it -- and we should name something — let’s be more like him,” Graham said.

By late Monday afternoon, Schumer himself appeared doubtful of the bill’s prospects, saying: “We’ve gotten some support. When will it be moved? Don’t know. Probably we’ll wait till after . . . I’ll have to figure . . . I don’t know yet.”

Asked whether he thought McConnell favored the bill, he said: “Ask him if he’s for it.”

Schumer said that he and Sen. Jeff Flake (R-Ariz.) had sent a letter to colleagues in a bid to round up support for the move. He declined to speculate as to the reasons for some lawmakers’ resistance to the plan.

“I think it’s the most appropriate way to honor Sen. McCain,” Schumer said.

Flake, the junior senator from Arizona, was one of the only Republicans to offer his full backing for the bill. “I want to be the first Republican co-sponsor for that resolution,” he told CBS’s “Face the Nation” on Sunday, adding, “I think that that would be a fitting tribute.”

In comparison, Democrats offered immediate support for the idea. “I think it’s a good idea,” said Sen. Bernie Sanders (I-Vt.), who caucuses with the Democrats.

The building currently houses a large marble statue of Russell as well as five committees and 36 senators’ offices, including McCain’s.

Tensions over how to commemorate the independent-minded senator served as a reminder of his ability to defy the GOP on key issues, something which McConnell alluded to in remarks on the Senate floor.

As McCain’s Senate desk lay draped with black cloth and white roses, he said: “If John saw an issue the same way you did, you knew you’d just found your most stalwart ally, you would thank your lucky stars.”

“Because when you found yourself on the other side of that table, as I think all of us learned, you were in for a different kind of unforgettable experience,” McConnell said.

“John and I stood shoulder to shoulder on some of the most important issues to each of us and we also disagreed entirely on huge subjects that helped define each of our careers,” he added.

Felicia Sonmez contributed to this report.