(CNN) Is Sen. Elizabeth Warren the first Democrat to beat Donald Trump at his own Twitter game?

In the past week the Massachusetts Democrat has refined an aggressive anti-Trump message through a series of so-called tweetstorms.

Whenever Trump criticizes her, Warren fires right back at him, sometimes twice as hard. Political pros are aflutter (or is that atwitter?) about it, and there are signs that the tweet-off will continue into the summer and fall.

The Twitter war resumed Wednesday with a back-and-forth about gender rhetoric, Trump's economic proposals and Trump's claim that Warren has accomplished nothing as a senator.

Goofy Elizabeth Warren has been one of the least effective Senators in the entire U.S. Senate. She has done nothing!

Do you think you're going to shut us up, @realDonaldTrump ? Think again. It's time to answer for your dangerous ideas.

The message: Challenge him where he lives (on social media), speak conversationally with blunt words like "loser," and "stand your ground."

In a tweet last Friday, she was explicit about this. Trump is a "bully," she said, but he can be defeated "not by tucking tail and running, but by holding your ground."

But here's the thing. You can beat a bully -- not by tucking tail and running, but by holding your ground. — Elizabeth Warren (@elizabethforma) May 7, 2016

The No. 1 purpose of Warren's tweetstorms, in the short term, is to urge sparring Democrats to unite behind a common enemy.

Warren, who is beloved by liberals, is perhaps uniquely able to weigh in because she has not endorsed Hillary Clinton or Bernie Sanders.

On Warren's personal Twitter account, @ElizabethForMA, none of her recent tweets have been about the Clinton-Sanders primary. In fact, the only person she has mentioned this month is: Trump.

(Warren's Senate account, @SenWarren, is separate.)

Warren, like many other legislators, devises her tweets and Facebook posts with help from aides.

She foreshadowed an anti-Trump strategy in March when she called him a "loser" with "failed businesses" and a history of corporate bankruptcies.

She fired back up May 3, minutes after Ted Cruz dropped out of the GOP primary race, leaving Trump as the party's presumptive nominee.

Her most-retweeted comment that night was: "There's more enthusiasm for @realDonaldTrump among leaders of the KKK than leaders of the political party he now controls."

Warren's comments were stitched together in a Facebook post. According to her office, the post received more than 45 million views on Facebook.

She mentioned that statistic on Friday night after Trump criticized her.

"I hope corrupt Hillary Clinton chooses goofy Elizabeth Warren as her running mate. I will defeat them both," he tweeted.

I hope corrupt Hillary Clinton chooses goofy Elizabeth Warren as her running mate. I will defeat them both. — Donald J. Trump (@realDonaldTrump) May 6, 2016

Within an hour and a half, Warren's response was up.

"He's so confident about his 'counter punch' he waited until Friday night. Lame," she said.

I called out @realDonaldTrump on Tuesday. 45 million saw it. He's so confident about his "counter punch" he waited until Friday night. Lame. — Elizabeth Warren (@elizabethforma) May 7, 2016

Trump had assigned her a nickname: "Goofy Elizabeth." So in her reply, Warren used Trump's December 2015 boast about knowing and having "the best words" against him.

"For a guy with 'the best words' that's a pretty lame nickname. Weak!" Warren tweeted, imitating one of Trump's favorite ways to finish a tweet, "Sad!"

Trump blasted Warren at a campaign rally that night and then continued on Twitter.

Goofy Elizabeth Warren and her phony Native American heritage are on a Twitter rant. She is too easy! I'm driving her nuts. — Donald J. Trump (@realDonaldTrump) May 7, 2016

She answered that one 45 minutes later:

No, @realDonaldTrump - your racism, sexism & xenophobia doesn't drive me nuts. It makes me sick. And I'm not alone. — Elizabeth Warren (@elizabethforma) May 7, 2016

For a few days, there was a cease-fire. But on Wednesday, the tweet-fire resumed.

In the morning Trump said Warren "has been one of the least effective Senators in the entire U.S. Senate" and that she "didn't have the guts to run for POTUS."

Goofy Elizabeth Warren has been one of the least effective Senators in the entire U.S. Senate. She has done nothing! — Donald J. Trump (@realDonaldTrump) May 11, 2016

In the early afternoon Warren responded with seven tweets in a row.

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

She sought to shift the conversation onto Trump's policy positions about the economy, one of her areas of expertise.

You care so much about struggling American workers, @realDonaldTrump, that you want to abolish the federal minimum wage? — Elizabeth Warren (@elizabethforma) May 11, 2016

You're so concerned about Wall Street, @realDonaldTrump, that you say you'd "absolutely" repeal Dodd-Frank? — Elizabeth Warren (@elizabethforma) May 11, 2016

Notably, Warren tagged Trump's Twitter handle in her messages, while Trump did not tag her handle. But later in the afternoon he confirmed that he'd seen her barrage of tweets.

Goofy Elizabeth Warren is now using the woman's card like her friend crooked Hillary. See her dumb tweet "when a woman stands up to you..." — Donald J. Trump (@realDonaldTrump) May 11, 2016

He sarcastically called her "our Native American senator" and said she "doesn't have a clue."

And so on it goes.