Andrew Harrer/Bloomberg via Getty Images "I've enjoyed your anti-Trump tweets," Hillary Clinton said. (OK, she didn't. This is an old picture.)

Twice this past week, Sen. Elizabeth Warren (D-Mass.) has unleashed a seemingly unprompted tweetstorm on Donald Trump, taking shots at the presumptive Republican presidential nominee for being sexist, a scam artist, "reckless" and "embarrassing."

Dripping with disdain, the 140-character asides got under Trump's skin (admittedly, not the hardest of feats). He accused her of "tweeting violently" and bestowed on the senator one of his trademark churlish nicknames. "Goofy Elizabeth Warren," he replied in tweets of his own.

The more important reaction came not from Trump, however, but from Hillary Clinton's campaign. Multiple sources close to the former secretary of state say that her aides took note of the senator's ability to rile the real estate tycoon. And they recognize the value of such dart throwing from, say, someone filling out a presidential ticket.

One close Clinton confidant said that she and her aides were "thrilled to see Warren get under his skin." Another senior Clinton adviser, who is advocating internally for Warren as a vice presidential pick, said the senator has “very influential people in the campaign pushing for her.”

A longtime Clinton veteran said the campaign definitely noticed Warren's attacks. "You want a running mate who can take the fight to the other side with relish," the veteran said. "Geography does not matter, but attitude and talent and energy and bringing excitement to the campaign, Senator Warren does all that."

.@realDonaldTrump: Your policies are dangerous. Your words are reckless. Your record is embarrassing. And your free ride is over. — Elizabeth Warren (@elizabethforma) May 11, 2016

We get it, @realDonaldTrump: When a woman stands up to you, you’re going to call her a basket case. Hormonal. Ugly. — Elizabeth Warren (@elizabethforma) May 11, 2016

Above: a sampling of the Warren tweetstorm against Trump

The attributes that Warren would bring to the VP slot extend beyond vigorous mocking of Trump. Top Democrats increasingly see a dual-female ticket as a potent response to a GOP nominee with a well-documented past of sexist remarks.

Then there is the conventional wisdom that Warren would keep backers of Sen. Bernie Sanders (I-Vt.) in the fold. "She can help validate Clinton with progressives and remind them that despite their differences in the primary, the alternative of the Donald would be untenable," said Penny Lee, a former longtime aide to Sen. Harry Reid (D-Nev.) and now a Democratic consultant.

As widely accepted as that argument is, it may dramatically understate the extent of Warren's appeal. In January 2015, pollster Peter Hart, who does survey research for NBC and The Wall Street Journal, ran a focus group in Colorado with independents and Republicans, gauging their outlook on the 2016 presidential election. This was not a set of millennial Bernie bros ripe for the political revolution. (In fact, Sanders' name never came up -- a window into just how far he's come in such a short time.)

What stunned Hart was the response to Warren. Not only was the group familiar with her, which took him somewhat by surprise, they were downright enthusiastic.

Asked to give one-word descriptions of a series of possible candidates, the focus group labeled most of them with terms like "liar," "failure," "fake," "two-faced," "crook," "not genuine" and "Lord Farquaad from Shrek." When it came to Warren, however, these moderates and conservative Republicans offered up words like "smart," "sincere," "interesting," "knowledgeable, intelligent," and "capable." Two of the 12 participants passed, a third said "unknown," and a fourth said "questionable." It was far and away the most positive response overall.

When Hart asked whom they would like to spend an hour with if they could choose from any of the possible candidates, six volunteered Warren above all others. "I saw her on TV, and she seemed very down to earth and knowledgeable, and I didn't know much about her," said one man in a typical explanation of his choice.

Hart then asked whom they'd like to have as their neighbor, if they had to have a politician living next door. Five of the 12 picked Warren. She was, several agreed, "the fun aunt."

Speculation that Warren would end up next to Clinton on the Democratic ticket this fall has been going on for months. But the extent to which Warren is being considered as the choice by the Clinton campaign remains relatively unknown.

In conversations with other top Democrats and close advisers to Clinton, it's clear that Warren's stock is rising. One Clinton adviser, who described himself as part of “Team Warren,” said that the idea had plenty of internal support and that the assumption Clinton doesn't like Warren personally is incorrect.

“Having been around Hillary when Elizabeth is talked about, there’s not much -- she doesn’t have bad feelings toward Elizabeth. It’s more that she’s frustrated that people don’t realize that she’s been championing these issues her whole life, too," the adviser said.

Moreover, the timing of Warren's attacks on Trump is being interpreted as a sign that she, too, is interested in the gig. Warren notably declined to rule out serving as Clinton's VP in a recent interview with Mic.

"She’s been a totally good soldier," said the adviser. "I understand that it’s to her benefit to stay out of the Hillary-Bernie thing -- talk about a no-win situation -- but you could say she’s already been auditioning for it a little bit," he said.

On Thursday morning, Politico reported that current Vice President Joe Biden thought Warren would be the best choice to replace him -- in what seemed like a well-timed leak to ensure just that.

J. Scott Applewhite/Associated Press They've sat next to each other before, when introducing then-Sen. John Kerry as a nominee for secretary of state.

But not everyone is certain that Warren would work as vice president or that she actually wants the job. The aforementioned close confidant interpreted the anti-Trump tweetstorm as more about Warren "showing other Democrats that this is the way to go after Trump, than about positioning herself as a VP candidate." Others, meanwhile, see a clear reason why she would take the post if offered.

Some who have tangled with Warren in the past suggest that she's a capable political talent but not deft enough to handle the crucible of a presidential campaign. Colin Reed, who works for the Republican super PAC America Rising and previously served as a top aide to then-Sen. Scott Brown, the GOP senator whom Warren defeated in the 2012 election, claimed that she underperformed President Barack Obama in Massachusetts by 15 percentage points that year. (Note: Warren got 53.7 percent of the vote in 2012, compared to Obama's 60.8 percent in the state, according to The New York Times, making the margin 7 percent.) Reed argued that Warren's brand as an anti-Wall Street populist would create tensions with Clinton that both of them would want to avoid.

"Warren castigates Goldman Sachs; Clinton takes their money," Reed said.

Eric Fehrnstrom, another former Brown adviser, had an additional theory as to why Warren was spending recent days composing anti-Trump tweets, one that suggested this was more about making amends than paving the way to the VP's residence.

"I think she needed to do something to take the pressure off herself because of her non-endorsement in the Democratic [presidential] race," Fehrnstrom posited. "The Hillary partisans, who are strong here in Massachusetts, have grown alienated because of her fence sitting. This was a good diversion for her. ... It spared her from answering the question of why, still at this late date, had she not endorsed Hillary Clinton."

A year after the Colorado focus group, Hart reached out to one of the women he'd met there. Jenny Howard, a conservative Republican, had stunned him with her positive opinion of Warren, which cut against everything he knew about Howard's politics. For all their differences, both Trump and Warren start from the belief that the system is rigged against the middle class, so Hart wanted to know if Howard had wound up in the Trump camp by the time the GOP race reached Colorado.

Not exactly. Instead, she told him, she was feeling the Bern.

Video produced by JM Rieger.

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This article has been updated with figures from the 2012 Massachusetts election results.