WASHINGTON — Understated. Self-effacing. Nonthreatening. Refreshingly old-fashioned.

Don’t let these cool descriptors from friends and colleagues fool you: As the vice president’s chief of staff, Bruce Reed plays Mr. Fix-It, guiding Joe Biden’s role as a driving force behind the Obama administration’s agenda.

With the White House wrestling Congress over gun control and tax-and-spending priorities, Reed’s deep ties to the Oval Office and reputation for getting along with both parties make him a central character in some of Washington’s biggest political battles.

Those who know Reed say his low-key style and consensus-oriented approach to deal-making are the keys to how he’s managed time and again to bridge an ever-widening gap between Democrats and Republicans — even when it rankles partisan Democrats who see concessions to the GOP as selling out.

“It gets characterized from an ideological perspective, meaning centrist vs. leftist. Bruce would probably see it more as, ‘Are you a reformer and willing to make changes to accomplish the same goals?”’ said Chicago mayor and former White House chief of staff Rahm Emanuel, who co-wrote a policy book with Reed after they served together in the Clinton administration.

It’s a trait that meshes well with the pragmatic, do-what-you-can approach to governing of President Barack Obama’s administration. Reed’s former and current colleagues say his method is also in sync with Biden’s freewheeling but driven personality.

Once considered a potential liability to Obama, Biden has evolved into a serious heavy hitter whose broad portfolio of issues is never far removed from the president’s top priorities. It was Biden, not Obama, who finally cut the New Year’s deal with the Senate that averted the so-called fiscal cliff. White House officials credit Reed, who turns 53 this month, with steering Biden away from political pitfalls, helping him gauge which battles to fight and just how far to push.

But Reed’s influence extends far beyond the vice president’s quarters and deep into the West Wing. He’s considered a full-fledged member of the economic team, joining the treasury secretary and others when the National Economic Council meets. Last year, he was tapped by Obama’s then-chief of staff, Bill Daley, to help coordinate the State of the Union address. When Biden negotiates with Republicans in Congress, Reed is often the only other person on the phone.

And when Obama’s most senior advisers meet every morning at 7:40 to set the day’s agenda, Reed is there. These mornings, it’s Reed who keeps Obama’s team up to date on one of the administration’s top priorities: gun control.

When the president tasked Biden with crafting a series of proposals to respond to a scourge of mass shootings, the role of chief architect fell to Reed, who cut his teeth on gun issues as Clinton’s domestic policy adviser. The ensuing proposal includes broadly supported measures like universal background checks, but also a controversial ban on assault weapons.

It quickly became clear the ban would face near-insurmountable obstacles in Congress. That led many to question whether the White House proposed the ban to placate those demanding tough action, but was ready to drop it if necessary to strike a deal. A Senate panel plans to vote on the ban Tuesday, though it has virtually no chance of passing the full Senate. While Biden and Obama say the ban deserves a vote, both have avoided describing it as a must-have.

“Nobody needed to tell me. I saw Bruce’s fingerprints all over it,” said former Clinton adviser William Galston, who met Reed in the late 1980s working on Al Gore’s first presidential campaign. “Bruce is not afraid of the politics of aspiration, but he has a healthy awareness of the distinction between the best and the attainable. He will not counsel people to fall on their sword.”

So far, there have been few outcries from the left over the prospect that the White House will abandon the assault-weapons ban — perhaps because even many Democrats are on the fence and fear being cast as infringing on lawful gun ownership.

On other issues where Reed has sought consensus with Republicans, the backlash has sometimes been quite public.

Credited with coining the phrase “end welfare as we know it,” Reed bore the wrath of liberals when he helped Clinton in 1996 secure a welfare overhaul — negotiated with Republicans — that ended some guarantees for poor Americans. A handful of Clinton officials resigned in protest.

Still, even those on the losing end of policy disagreements say Reed somehow manages to keep it from getting personal. Peter Edelman, one of the officials who resigned, said even when consensus proved elusive, Reed treated his adversaries with respect.

“In all the years I worked with him, I only saw him lose his temper once at me,” said Paul Weinstein, an economist who has worked for Reed in various roles since the 1980s. The rare outburst came in 1992, near the end of Clinton’s campaign, when Weinstein told Reed he needed to step away from the campaign to finish his Ph.D. “Bruce just lost it on me,” Weinstein said. “When I tell people I saw him lose his temper, they practically fall over backwards because they don’t believe it.”

Democratic strategist Kiki McLean, who has known Reed for more than two decades, said his sense of humor is striking considering his unobtrusive manner. “Bruce is not the guy who will stand on the table and sing, but he is the guy who will lean over and whisper something so you have to hold your sides to keep from bursting out laughing,” she said.

Raised in Coeur d’Alene, a small Idaho town near the Washington state border, Reed followed his mother, Mary Lou Reed, a Democrat and former Idaho state senator, into politics. He moved east for school, studying English at Princeton University before becoming a Rhodes Scholar and earning a master’s degree at Oxford University. An avid baseball fan, Reed proposed to his wife, attorney Bonnie LePard, at a Pittsburgh Pirates game; they have two children.

He wrote speeches for then-Sen. Al Gore, D-Tenn., starting in 1985, then joined the Democratic Leadership Council, a now-defunct group that sought to push the Democratic Party toward the political center. He served for all eight years in the Clinton White House, where he was often the public face of the administration’s policies on education, guns and welfare reform. Later, he ran the Simpson-Bowles commission, tasked with forging a bipartisan deficit-reduction deal.

That deal never made it to a vote in Congress, but Reed impressed lawmakers from both parties. Republican Sen. Mike Crapo of Idaho, a vocal critic of Obama, recalled how Reed would flesh out a lawmaker’s idea, providing the analysis and figures needed to fully evaluate it.

“It happened again and again,” Crapo said. “Even if it wasn’t necessarily something he would support from his personal political perspective, he was very focused on helping the individual member.”

It’s been just over two years since Biden tapped Reed to be his chief of staff, and his cautious and meticulous manner often serves as a counterweight to the more verbose and unrehearsed Biden. In that short time, Biden has played a leading role in winding down the war in Iraq, negotiating a fiscal-cliff deal with Senate Republicans, nudging Obama toward an embrace of gay marriage and spearheading Obama’s push on gun control.

Reed declined to be interviewed for this story. But Galston, the former Clinton adviser, said Reed values clarity of expression above almost all else.

“He edits documents the way a sculptor works with a block of marble: by subtraction,” said Galston. “You get rid of what you don’t want, and what’s left is what you have in mind.”