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.

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