Secretary of State Hillary Rodham Clinton told CNN on Monday that she takes "full responsibility" for security issues in Libya leading up to the attack that claimed the lives of four Americans there last month. In doing so, she added to the already considerable impact of the Clinton name on this election.

Here's why Clinton's statement matters politically, even if politics wasn't the main factor in her decision: Republicans have been up in arms since the Sept. 11 attack in Benghazi, noting security requests that went unmet in the lead-up to the assault, and a shifting explanation of the violence by the Obama administration, which first called it spontaneous before later saying it was an act of terror.

Clinton went a step further Monday -- the eve of a crucial presidential debate -- than she did in answering questions about possible security lapses in Benghazi in part because of the impression that Vice President Biden had left in his own debate with Rep. Paul Ryan (Wis.) last week.

Clinton was clarifying that it's the State Department, and ultimately the secretary of state, that bear responsibility for what amounted in this case to a fairly routine personnel decision. But she also was shouldering a political weight that had seemed to shift from the State Department to the White House over the preceding days. Republicans have pointed their fingers directly at President Obama, while his aides have sought to shift the blame to Foggy Bottom.

“I think what [Biden] was talking about was what he and the president knew, because these matters were being handled at the State Department,” Obama campaign adviser David Axelrod said in a Sunday interview. Axelrod was responding to a question about the vice president, who said at the debate that “we weren’t told they wanted more security there.”

In the aftermath of situations like the one in Libya, it isn't uncommon for the different government agencies involved to cover themselves by (often anonymously) blaming other agencies. But in this case, Clinton absorbed the blame head on.

Her decision does two things. One, it takes some pressure (but not all; Obama is still the president, and national security starts and ends with him) off the president and shifts it over to Foggy Bottom.

Second, when Republicans attack the administration now, they also will have to go after Clinton more directly, which is a dicier political proposition than taking on Obama. Clinton is arguably the most popular member of the president's cabinet. Earlier this spring, her approval rating stood at a remarkable 65 percent in a Washington Post-ABC News poll.

There are other reasons Clinton can afford to do this. Not only is she the top of the paper chain at the State Department, she also is pretty much bulletproof on Capitol Hill. There hasn't been any real clamor for her to testify, or otherwise be chastised.

Three Republican senators who sit on the Armed Services committee reacted to Clinton's comments with a statement Monday that sought to keep the focus on Obama.

“We have just learned that Secretary of State Hillary Clinton has claimed full responsibility for any failure to secure our people and our Consulate in Benghazi prior to the attack of September 11, 2012. This is a laudable gesture, especially when the White House is trying to avoid any responsibility whatsoever," said Sens. John McCain (Ariz.), Lindsey Graham (S.C.), and Kelly Ayote (N.H.), who added, "The security of Americans serving our nation everywhere in the world is ultimately the job of the Commander-in-Chief. The buck stops there."

The secretary of state's decision to help Obama is far from the first time a Clinton has come to the president's defense at a time he needed it most this cycle. Popular as ever, former president Bill Clinton already has cemented his presence as Obama's single most important surrogate. He's cut ads defending the president and brought electricity to the Democratic National Convention in Charlotte. He's also been hitting the campaign trail for Obama, and if that's not enough, he released a video Tuesday morning slamming Republican challenger Mitt Romney's tax plan.

What a difference four years makes. It wasn't long ago that the Clintons and Obama were furiously going after one another in the heated 2008 Democratic presidential primary.

As Hillary Clinton prepares to step down from her role as the nation's chief diplomat next year, she's expected to do so in sound political shape, prompting chatter about the possibility that she would make another run for president in 2016. The fallout from the situation in Libya could ding her image in the short run, but supporters are confident it will be ancient history by then.

Clinton has no stellar accomplishments like a Mideast peace deal to her credit as secretary, but she is still among the most admired occupants of that job, ever. She is widely credited, including by Republicans, with improving America's image in the world. But now she has a tragedy on her watch in a country she had taken a direct personal interest in, and where the Obama administration had claimed a policy success in the confusing aftermath of the Arab Spring.

As to the the current presidential election, it's about Romney versus Obama. But in many ways, its been about Romney versus the Clintons and Obama. For his part, the president  who at times has struggled to effectively deliver his own message, has no doubt welcomed the assistance with open arms.

-- Anne Gearan contributed to this post 

Updated at 1:30 p.m.