Sen. Cory Booker's (D-N.J.) name comes up frequently in talk about the 2020 presidential race, but some Democrats wonder if he has what it takes to compete in what could be a crowded primary.

While Democrats say Booker, 48, is one of the party's "fresh faces" compared to elder statesmen like former Vice President Joe Biden and Sen. Bernie Sanders (I-Vt.), they aren't sure he has created a lane for himself against would-be rivals.

"It's a very high ceiling but he hasn't met early expectations," said one top Democratic strategist who has worked on several presidential campaigns. "He needs a signature fight or issue to really differentiate himself."

Booker - who is known for his nonstop Twitter presence and his touchy-feely speeches - hasn't quite captured the attention of party insiders and big donors, many Democrats say. And there's a fear he may be a little too soft for the party's white-knuckled approach against President Trump.

"There's a reputation that's maybe unfairly adhered itself to him of being a gadfly, a show horse, not a workhorse," the strategist added. "Some of it happens because he gives a good speech and seems to relish social media."

Patrick Murray, the director of the Monmouth University Polling Institute in New Jersey, put it this way: "He is someone who thinks about the issues but he's not somebody who is going to fork through every line of the budget."

Booker's office did not respond to a request for comment on this story.

But in an interview earlier this year on "The Ezra Klein Show," Booker acknowledged that Democrats want him to be a little tougher.

"Democrats all the time, where they say, 'Enough with the love and kindness stuff, Cory. We've got to fight.' And I say, 'When are those mutually exclusive?' "

"I think again we lose a bit of our moral compass when we are demonizing people. I just don't believe you need to be mean, you need to be deceitful, you need to proactive the dark arts in order to win elected office," he said.

Booker is seen in different lights by centrists and progressives in the party.

The increasingly energized progressive wing of the party sees him as too pro-business.

Booker has long-running ties to Wall Street. In the 2013-14 election cycle, he filled his coffers, raising nearly $2 million from the investment and securities industry - bringing in more from the industry than any other candidate.

Progressives also point to the time then-President Obama went after 2012 Republican presidential nominee Mitt Romney regarding his ties to Bain Capital. Instead of agreeing with Obama, Booker called the Obama campaign's attacks "nauseating" and "ridiculous" in an appearance on NBC's "Meet the Press."

Centrists believe he's trying to reinvent himself as a progressive.

This summer he announced that he was backing Sanders's single-payer health-care proposal. He also began advocating for the legalization of marijuana and introduced an environmental justice bill.

The effort was clearly aimed at increasing Booker's appeal with progressives.

Advocating for the legalization of marijuana in particular "signaled a desire for an eventual candidate Booker to have a case to make to millennials," said Brigid Callahan Harrison, a professor of political science and law at Montclair State University.

But some Democrats think the move to the left isn't a good one for Booker, given rivals who will be clear favorites with that part of the party.

"He'd be smart not to try and chase Bernie Sanders and [Sen.] Elizabeth Warren [D-Mass.] to the left, and rather use his background of taking some centrist pro-business positions to differentiate himself from the pack in what could be a fragmented primary," said Jon Selib, a Democratic strategist who served as chief of staff to former Sen. Max Baucus (D-Mont.)

The top Democratic strategist agreed that it may be tough for Booker to win over progressives in a race against the likes of Warren and Sanders.

"I can't see progressives letting him out of the primary," the strategist said. "They see him as too close to Wall Street, too willing to go bipartisan when a fight would be more appropriate," the strategist said. "To make a vast understatement, someone whose instincts are to go middle-of-the-road in a moment that calls for a revolution is going to have a tough time."

Booker remains an attractive candidate who is relatively well-known.

A poll out last month from the University of New Hampshire showed that Booker trailed Biden, Sanders and Warren in a survey among Democratic voters.

The former mayor of Newark has been known to respond to curses from critics on Twitter with a simple "I love you."

Last year, for example, then-presidential candidate Trump took to Twitter to attack Booker.

"If Cory Booker is the future of the Democratic Party, they have no future! I now more about Cory than he knows about himself."

Booker responded with a simple "I love you, I just don't want you to be my president."

"I think he has a lot of potential in 2020 because he is an inspirational figure," Selib said. "There are a lot of elements in his story in Newark that are great to tell - I mean, he's run into burning buildings and lived in a housing project - and that's a great contrast with Donald Trump, who has no idea what it's like to be middle class."

Booker has "walked the walk in a way few politicians have done," he added.

He got some props from Democrats in January when he testified against now-Attorney General Jeff Sessions - a move that made him the first sitting senator to testify against a fellow senator's cabinet nomination.

The junior senator may have also gotten a light endorsement of sorts from Donna Brazile, the former interim chief of the Democratic National Committee, who wrote in a new book that she had briefly considered replacing Hillary Clinton and running mate Tim Kaine with a Biden and Booker ticket.

"I think it played well in the sense that he didn't see it coming and what it continues to do is to portray him as the future of the Democratic Party," Murray said.

Harrison dismissed the criticism that Booker is a "lightweight."

"People confuse his social media presence with a flighty personna," she said. "But if you listen to him beyond 140 characters you have to be impressed by the substance of what he says."

Harrison said his soaring speeches and more gentle and bipartisan approach might also work to his advantage.

"In this political climate, boy isn't that something that is really appealing right now?" she said.