(CNN) On the campaign trail, Alexandria Ocasio-Cortez turned herself into a phenomenon. So far it's been the same in Congress, where she's using her star power to turn ordinarily dry hearings into viral, must-see TV.

This week her target -- well, one of them -- was campaign finance. Seated at a big leather chair, she went on the attack like she was back on the stump, whipping through a fierce argument about Washington's influence machinery that got retweeted and described as "just sensational" by late-night host James Corden

By Friday afternoon, she was getting invited to watch the Grammys with Chrissy Teigen, who called her "my hero."

yes! we can live-tweet me burning something in the kitchen

The episodes capped a week that started with Ocasio-Cortez being photographed striding into the House chamber for the State of the Union, wearing a white cape that appeared to awe a group of starstruck young men.

She then debuted the Green New Deal resolution , her first major legislative proposal, alongside Sen. Ed Markey -- a Massachusetts Democrat who's been in Congress for longer than she's been alive. The launch further stoked a suddenly riveting debate over climate change and jobs programs, which landed on the front page of The New York Times.

While the fate of the Green New Deal remains a long way off, Ocasio-Cortez has consistently defied critics from both parties who at times seem to be tripping over each other to question her tactics, especially her aggressive use of social media. Ocasio-Cortez's communications director and longtime aide, Corbin Trent, said the Bronx-born congresswoman has no plans to change -- that Twitter and Instagram were key tools for galvanizing the public support that ultimately inspired a handful of the party's top presidential hopes to back the resolution.

"The way she operates, whether it's to come up with lines of questioning or lines of messaging, or how to present things to her constituents or to the American people or to the party -- it's continuous listening and talking," Trent told CNN. "When she using social media, that is essentially a practice run and a conversation that she's working and developing."

Rep. Jamie Raskin, a Maryland Democrat, said Ocasio-Cortez represents "a classic story of how somebody gets assimilated into the institution while preserving all their values and desires for change."

"I think it's been a wonderful transition to see someone go from being a full-time activist to being a legislator and an activist," he said.

Pelosi's relationship with Ocasio-Cortez has, to date, been mutually beneficial. Ocasio-Cortez helped secure the California liberal's left flank amid a leadership challenge. Pelosi, even while denying the New Yorker a new select committee assignment that would have been dedicated specifically to shaping the Green New Deal, offered her a seat on a different climate panel.

Ocasio-Cortez turned down the offer, citing the time she needed to manage her other assignments. Their relationship now is less a fight than a dance.

Asked on Thursday about Pelosi's description, in a Politico report, of the Green New Deal as "the green dream or whatever they call it," Ocasio-Cortez passed up a chance to land a jab.

"No, it is a green dream," she told reporters. "I don't consider that to be a dismissive term."

Even as her profile -- and influence -- rises, Ocasio-Cortez operates much as she did on the campaign trail. During a visit to the Midwest last summer to stump for other progressive hopefuls, Ocasio-Cortez would unleash her fire at the mic but then move quietly backstage at events, jotting in her notebook, constantly updating her speech with a new line or idea.

"What we're seeing is that there is not one single way to get things done," Trent said. "She was saying today, everybody says this is the way things are done in Washington and there certainly is a way things have been done in Washington, and there are certainly people who are going to continue to work that way. And I'm sure they'll be able to get things done. But there are also other paths."

Rep. Brenda Lawrence said Ocasio-Cortez and other new members who came in as activists are learning how to operate in a deliberative body.

"It's one thing to protest. It's another to pass laws and bills and actually impact lives and make a difference," said Lawrence, a third-term Michigan Democrat who co-chairs the bipartisan Women's Caucus. "So she's at the beginning of that. And I'm excited. She's going to have some growth and some bumps in the road."

"Every step is growth," she added. "She has such a large media platform, which I pray continues to be a positive one and continues to be one of the boldness of speaking truth to power."