By Lauren Fox, CNN

(CNN) -- Senate Minority Leader Chuck Schumer will introduce a resolution to rename the Senate's Russell office building after the late Sen. John McCain.

In a statement Saturday night, a short time after McCain died, Schumer said, "Nothing will overcome the loss of Senator McCain, but so that generations remember him I will be introducing a resolution to rename the Russell building after him."

"As you go through life, you meet few truly great people. John McCain was one of them," Schumer said. "His dedication to his country and the military were unsurpassed, and maybe most of all, he was a truth teller -- never afraid to speak truth to power in an era where that has become all too rare. The Senate, the United States, and the world are lesser places without John McCain."

While President Donald Trump signature would not be required to change the name of the Russell Senate Office Building nor would the House vote on it, the effort could test Republicans' resolve against the sitting President. On the presidential campaign trail Trump questioned McCain's credentials as a war hero and has since often attacked the Vietnam War veteran, calling him out at rallies for voting against a proposal that would have advanced the GOP's effort to partially repeal the Affordable Care Act.

While it's unclear whether the President would oppose renaming one of the Senate's three office buildings after McCain, a showdown over the renaming could lead some Republicans to have to choose which side to stand on.

Schumer's call to rename the storied Senate office building after McCain was a nod to the deep, bipartisan friendships McCain amassed throughout his career in the Senate.

A top Republican leadership aide was unaware of Schumer's proposal and told CNN it would take time to research it before commenting.

The Russell building is currently named after former Georgia Democratic Sen. Richard Brevard Russell, who served from 1933 to 1971. A segregationist who vehemently opposed the Civil Rights Act, Russell at one point served as president pro tempore -- a ceremonial designation bestowed on the most senior member of the party in power.

Russell, who served for nearly four decades, was known as a student of Senate rules and famously deployed them in his opposition to civil rights. He helped write the Southern Manifesto, which outlined congressional opposition to racial desegregation. According to the Senate's own website, the Russell Senate Office Building was known simply as the Senate office building until the Dirksen building was constructed. After that, lawmakers referred to it as the old Senate office building until it was named for Russell in the 1970s.

Schumer's announcement came as remembrances and condolences for McCain's family poured in from both sides of the aisle. In his statement, Majority Leader Mitch McConnell said McCain's death represented a "sad day for the Senate and for our nation."

Former Vice President Joe Biden, a former senator and colleague to McCain, said, "John McCain's life is proof that some truths are timeless. Character. Courage. Integrity. Honor. A life lived embodying those truths casts a long, long shadow. John McCain will cast a long shadow. His impact on America hasn't ended. Not even close. It will go on for many years to come."