WASHINGTON (AP) – A proposal to rename the Russell Senate Office building after Sen. John McCain appears to be gaining bipartisan support, but success is far from assured.

Senate Democratic leader Chuck Schumer proposed renaming the Senate’s oldest office building in McCain’s honor after the Arizona Republican died Saturday from brain cancer.

Republican Sen. Chuck Grassley of Iowa, who served with McCain for 31 years, says he’s in favor of “naming almost any building” for McCain, but adds, “I’m not sure that I would make a decision on a specific building at this point.”

The building is named after Sen. Richard Russell, a Georgia Democrat who, like McCain, chaired the Armed Services Committee.

Russell was a segregationist and led Southern opposition to anti-lynching bills and other civil rights legislation. He died in 1971.