WASHINGTON — Thirty minutes into a meeting with top White House officials, Elizabeth Warren stopped fiddling with her pen and began pressing President Obama’s aides to be more aggressive with the health insurance industry.
“There is a law — it’s not a question of ‘do we need to get a law passed on our side,’ ” the Massachusetts senator said Wednesday, seated in an ornate conference room down the hall from the vice president’s offices. “We need the law enforced.”
“Let me ask another question,” she said, pressing the point even though the president’s staff reminded her and other lawmakers there that a handful of reporters were watching. “Are there any plans to prosecute the insurance companies?”
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Warren’s detractors call it grandstanding. But her habit of needling, and sometimes flat out taking on, her own party when it veers toward the political center is what Warren’s allies love about her. And it’s exactly the trait they worry she’d have to give up if she abandons her perch as a senator and becomes Hillary Clinton’s running mate.
The question among her supporters on the left is this: Would Warren actually lose power by becoming first in line to be president?
“When you’re vice president, it’s not your agenda, OK. It’s the president’s agenda,” former vice president Dan Quayle said in an interview with the Globe. “That is something significant you are giving up. That independence.”
Quayle said he got prime presidential access as part of the trade-off. “You’re right there. You’ve got the office very close to the Oval.”
But on those occasions when he disagreed with the boss, President George H.W. Bush, discretion was at a premium. “I did it privately. It is a mistake if you do it publicly. Because you are a team.”
Being a team player may not come naturally to Warren, one of the party’s most outspoken stars. Nevertheless, Quayle suspects that if the post is offered, Warren will say yes. “People don’t turn it down,” he said.
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Speculation about others who might be tapped by Clinton focuses mostly on a group of male politicians, including Senators Tim Kaine of Virginia, Sherrod Brown of Ohio, and Cory Booker of New Jersey. Also frequently mentioned: Housing Secretary Julian Castro and Labor Secretary Thomas Perez.
Some of the liberals who have long backed the Massachusetts senator say they’re torn about the idea of a Vice President Warren, particularly because she would be subordinate to Clinton, a leader who hasn’t completely earned their trust.
And because Warren has a reputation of speaking her mind, there are people close to Clinton who think she would be difficult to control and therefore lacks the temperament for the number two slot.
“When Warren is in the Senate, you know she is going to be a fighter,” said Neil Sroka, spokesman for Democracy for America, a liberal group that tried to draft Warren to run for president.

He added that she’d be valued there in the future for her “voice of opposition on issues — if they were to come up — in a Clinton White House.”
Clinton’s campaign team hasn’t said anything official on potential vice presidents, though speculation spiked that the Massachusetts freshman senator could be on the ticket when the two women sat down for a meeting shortly after Warren endorsed Clinton last week.
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Warren, on Friday, stoked those rumors when she stopped by Clinton’s Brooklyn campaign headquarters and exhorted the staff, “Don’t screw this up!”
Warren is by far the most popular pick among Democrats, with 35 percent selecting her as their first choice to complete the ticket, according to a Bloomberg Politics poll. Booker came in second with 17 percent.
Warren’s done little to tamp down the speculation. When asked by MSNBC’s Rachel Maddow if she feels she’d be ready to be president if something happened to Clinton, the senator replied: “Yes. I do.” And two of Warren’s advisers have told the Globe that she’s intrigued with the idea.
On Saturday, Warren rallied the troops, giving a speech to the party faithful at a Democratic Party event in Bedford, N.H., her first trip to the first-in-the-nation primary state in nearly two years. “Whether we supported her in the primary or not, we can all say Hillary Clinton is a fighter,” Warren told the crowd.
Warren declined to be interviewed for this story.
Barney Frank, a Clinton ally and former representative from Massachusetts, predicted that Warren as vice president would carve out a role for herself as the tsarina of financial rules in a Clinton White House.
“It would be a natural fit for Warren to be the coordinator for financial regulation and reform,” Frank said. “It would be such an obvious fit for her.”
He said he’s not worried about her being sidelined in the number two job. “She would have a broader and deeper impact on public policy, particularly on the issues she’s most concerned about,” Frank predicted.
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There’s no shortage of historical precedent for discomfort at the vice presidency’s combination of very high profile and minimal actual power.
Yes, you get an airplane, a mansion, a motorcade, a special seal, and a flag. But you’re also in a job once described by the late historian Arthur Schlesinger Jr. as “a doomed office” in which the occupant’s main role is to “wait around for the president to die.”
John Nance Garner famously regretted giving up his powerful role as House speaker for the vice presidency under Franklin Roosevelt, a job he later said “wasn’t worth a pitcher of warm spit.” President Dwight D. Eisenhower, when asked what major decisions his vice president, Richard Nixon, participated in, famously replied: “If you give me a week, I might think of one.”
Then there’s the example that liberals fear most: Hubert Humphrey. Like Warren a darling of the left, he was tasked by President Lyndon Johnson with defending America’s role in Vietnam, which put him in direct conflict with his former allies and hobbled him when he sought the presidency himself.
In more recent times, the vice president has had a more robust role — but those models wouldn’t necessarily work in a theoretical Clinton-Warren pairing.
Dick Cheney, one of the most powerful vice presidents in modern history, found room to maneuver (particularly in George W. Bush’s first term) because he served an executive who had less experience and comfort with the vast federal bureaucracy.
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Joe Biden, the current vice president, blazed a path to power as Obama’s buddy. The two didn’t start with a close relationship, but Biden’s deep knowledge of government and his relationships on Capitol Hill after 36 years in the Senate helped him forge one, said Ted Kaufman, Biden’s longtime chief of staff who took over his Delaware Senate seat when Biden moved into the vice presidential mansion.

“The presidency now is so incredibly complex that you need a partner,” Kaufman said. “You just have to have a partner.
“The big advantage for Biden, and for Warren, is she could really advance and have a real impact on the issues she cares about,” Kaufman said.
Still, it was “very hard” for Biden to give up his independence, Kaufman said.
It’s not an issue everyone struggles with.
John Edwards was not seeking reelection to his Senate seat when John Kerry selected him for the 2004 Democratic ticket.
“Edwards was dying for the job,” recalled David Wade, a top staffer for Kerry.
“He was campaigning for a second act in politics and a chance to have eight years in the White House and a national future,” Wade said. “It was a seller’s market, and Kerry wanted to know whether Edwards could be a loyal wingman in the White House and put his own ambitions on hold.”
If the vice presidency has changed, so has the Senate.
Warren’s ability to be effective in a legislature that’s become markedly more partisan over time has limits that previous senators didn’t have to contend with.
There’s partisan gridlock on the most basic of votes, a continual need to raise money for the next campaign, and far less time or appetite for actual governing.
That means seizing the role as a legislative leader in the mold of other influential Massachusetts senators is far more difficult.
“She has really quickly assumed that Ted Kennedy mantle to the party faithful,” said Scott Ferson, a Democratic strategist. “You could see her going around the country rallying the troops.
“The other part of Ted Kennedy, being effective on legislation, is an era that’s passed.”
James Pindell of the Globe staff contributed to this report. Annie Linskey can be reached at annie.linskey@globe.com. Follow her on Twitter @AnnieLinskey.