Not every Republican agrees. Mitt Romney, who has opposed the flag before, issued another well-circulated call to take it down on Saturday.
As did a key religious conservative. "That sort of symbolism is out of step with the justice of Jesus Christ," wrote Russell Moore, a leader in the Southern Baptist Convention.
Ohio Gov. John Kasich, who is considering a presidential run, released a statement Saturday saying:
"This is up to the people of South Carolina to decide, but if I were a citizen of South Carolina I'd be for taking it down."
South Carolina state Rep. Norman Brannon (R) said Friday night he'll introduce a bill to remove the flag from capitol grounds. But Republican politicians like Romney and Brannon have also faced pushback when they've sided with getting rid of the flag.
"That's opening up Pandora's box," Rep. Mark Sanford (R-S.C.), a former governor of the state, said when asked on MSNBC if it should be taken down.
The fight over a Confederate emblem
"If you touch it, you usually die politically," Scott Buchanan, a political science professor at The Citadel in South Carolina, told The State newspaper in 2014.
The Confederate flag, of course, first experienced its resurgence in the then-heavily Democratic South. Today, though, Democrats are much more likely to oppose it, making it a pretty easy call for Democratic politicians.
But for the least two decades, it's an issue which has divided and tripped up many Republicans.
When asked in a 2007 CNN/YouTube presidential primary debate about the flag, the Massachusetts governor said "That's not a flag I recognize."
"That flag, frankly, is divisive, and it shouldn't be shown," he said.
In response, the Americans for the Preservation of American Culture ran several radio ads hitting Romney in the South Carolina primary for not supporting the state's heritage.
When Sen. McCain (Ariz.) first ran for president in 2000, he said the flag "was a symbol of racism," then reversed course, releasing a statement saying he actually thought the flag was "a symbol of heritage."
“I feared that if I answered honestly, I could not win the South Carolina primary,” McCain said back then.
He later regretted defending the flag. Since then, McCain is perhaps the most vocal Republican critic of the Confederate flag -- and he paid for that, too.
"I can't be more proud of the overwhelming majority of the people of this state who came together in taking that flag off the top of the Capitol," the 2008 GOP presidential nominee said while campaigning in South Carolina that year. (The flag originally flew directly over South Carolina's state house but in 2000 was moved to a nearby Confederate War memorial.)
That earned him radio ads from -- guess who? -- the Americans for the Preservation of American Culture. Pro-Confederate flag protesters would show up to his campaign stops in the south, carrying signs that read "The South does not want John McCain."
Sen. Paul (Ky.) hasn't specifically gotten in trouble for expressing his views on the Confederate flag. But in 2013, the conservative Washington Free Beacon revealed one of Paul's social media aides had worn a Confederate flag mask while writing about his support for the Confederacy and secession under the nom de plume "Southern Avenger."
The 2016 presidential candidate was forced to publicly defend his aide and Paul's decision to keep him on staff.
"Are we at a point where nobody can have had a youth or said anything untoward?” Paul said.
In the same presidential 2007 debate that tripped up Romney, former senator Thompson (Tenn.) also faced backlash for his comments. He said: "As far as a public place is concerned, I am glad that people have made the decision not to display it as a prominent flag -- symbolic of something -- at a state capital."
The next week in South Carolina, CNN reported Thompson was met by "eight Confederate-flag waving men" wearing Confederate flag jackets and holding signs that said, "The South hates Fred Thompson."
Massachusetts Gov. Charlie Baker
Massachusetts' newest governor is perhaps the most recent politician to stumble over the Confederate flag issue. In a radio interview with Boston's WGBH on Thursday, Baker said states should be allowed to choose whether to fly the flag on their capitol grounds.
But he pulled a 180 later that day after he "heard from some friends of mine" who asked him, "What were you thinking?"
He apologized in an interview with the Boston Globe. "I think they should take the flag down,” he said.
South Carolina state legislators
In the 1990s, as other Southern states slowly lowered their Confederate flags, South Carolina's remained in place. Local business leaders were concerned about the message their lonely Confederate flag sent to national companies, so the local Chamber of Commerce threatened Republican state legislators with cutting off campaign contributions if they didn't acquiesce to lowering the flag.
That didn't go over well with the GOP lawmakers, the New York Times reported in 1999.
"I'd like to tell you one thing," lawmaker Jake Knotts (R) said. "The Confederate flag's not for sale here."
South Carolina Gov. David Beasley
As the debate in South Carolina continued over the Confederate flag, Beasley became just a one-term governor in part thanks to it.
The devout Christian said he had a change of heart while reading the Bible. In 1996, he made a very public speech calling for the removal of the flag from the capital. He lost his 1998 reelection bid -- in part, analysts argue, because conservatives who supported the flag stayed home.
Politicians avoiding trouble
The states-rights argument Baker tried to make might not have worked in the Northeast. But nationally, several GOP politicians have successfully navigated their way out of trouble with it.
In 2000, then-presidential candidate George W. Bush said it's up to each state to decide. That was "an acceptable stance to pro-flag groups at the time," the Washington Times reported. (Also, Bush won the nomination and became president.)
In 2012, meanwhile, former House speaker and GOP presidential hopeful Newt Gingrich (Ga.) earned loud cheers from a South Carolina crowd when the presidential candidate said flying the flag on state grounds is "up to the people of South Carolina."
And back in 1993, George Allen ran for governor of Virginia with a TV ad that included a Confederate flag. He defended himself from criticism from black lawmakers, saying the flag was a symbol of Virginia's heritage as the capitol of the Confederacy. He also said that he once displayed the flag at his log cabin, but that he took it down before his campaign to avoid offending anyone. Allen won the election.