Updated

It didn’t take Democrats long to get in their shots at potential 2016 presidential candidate Chris Christie, suggesting within hours of the New Jersey governor’s landslide re-election that he will be an absentee leader who won on personality and the serendipity of Superstorm Sandy.

Apparently adding to the swipes was the cover of Time magazine’s latest issue, made public on Thursday, which depicts a silhouette of the hefty governor with the headline, “The Elephant in the Room,” a title perceived by some as a slight about Christie’s weight.

The political attack lines emerged soon after Christie’s victory speech on Tuesday night, in which the second-term governor said he would “never stop leading the state he loves.”

Top Democratic Party strategist David Axelrod was the first to chime in via Twitter, just minutes after Christie finished speaking: “But, pretty clearly, he's going to be LEAVING NJ quite a bit between now & '16.”

By Wednesday morning, Florida Rep. Debbie Wasserman Schultz, chairwoman of the Democratic National Committee, hinted at the party’s primary attack line, saying Christie’s 22-point victory over Democrat Barbara Buono was the result of his charisma and the opportunity to respond to a natural disaster - the deadly 2012 superstorm that made a direct hit on New Jersey.

“You cannot attribute this to anything more than a big personality and the aftermath of the storm,” she said on one cable news show.

Wasserman Schultz also cited New Jersey’s 8.5 percent unemployment rate, an indication of how Democrats might continue to hammer away at Christie’s qualifications. Wasserman Shultz failed to point out that in neighboring New York state – led by Democratic Gov. Andrew Cuomo – the unemployment rate is actually higher, at 8.7 percent.

Time did not immediately return a message left by Fox News on Thursday about the cover. But according to a post on the magazine’s website, “the overarching themes of the package: Christie’s outsized influence in his party and the discomfort he causes some fellow Republicans who consider him, well, the elephant in the room.”

However, condemnation of the cover for its perceived weight insinuation came from across the political spectrum.

“Whether or not one likes Christie, these cheap shots – like Time’s new cover – about his weight are decidedly uncool,” New York Times reporter Steven Greenhouse posted on Twitter.

“You have to admit: that’s some dang good passive-aggressive, plausibly deniable fat-shaming, there,” RedState’s Moe Lane said.

Allen Steadhman, the director of the International Size Acceptance Association, which looks to combat discrimination against heavyset people and educate about health and weight, told Fox News the cover helps perpetuate backlash against people of large body sizes.

“It’s the cheapest route to get attention,” Steadham said. “They’re definitely making use of the word ‘elephant’ in a negative way that alludes to his weight.”

In Washington, by Wednesday afternoon Democrats were advancing Wasserman Schultz’s talking points, repeating the claim Christie won on personality and the emotional connection to his Sandy-recovery efforts.

They also raised doubts about whether Christie could sustain the energy of his big win, or transfer it to other GOP candidates. Some Democrats predicted he would follow the path of former New York City Mayor Rudy Giuliani, who vaulted to national prominence for his handling of 9-11, but failed convert that popularity to success on the national campaign trail.

Christie won, “I think, yesterday based on the force of his personality … as well as an emotional connection to the Sandy relief,” Mo Elleithee, Democratic National Committee communications director, told reporters in a teleconference. “I don't think that is transferrable to the party or other candidates, nor is it sustainable.”

Elleithee alsodescribed Christie’s run as a “Giuliani boomlet” in which people say, “Oh here's a Republican who knows how to win in blue territory after, in part, some sort of an emotional connection to a national tragedy. It's not transferable and it's not sustainable."

New Jersey Democrats began complaining long before election night that Christie has already begun governing with an eye on the White House.

They suggested he vetoed an obscure bill on pig crates that was backed by animal rights activists because Iowa – home to the first election event in the presidential nominating process - is the country’s top hog-producing state.

Christie’s office said the governor thinks the State Board of Agriculture and the Department of Agriculture can better develop and adopt such standards that balance farmers’ financial interests with the humane treatment of livestock.

But not all Democrats were willing to take shots at Christie, particularly not those in the Garden State who had endorsed him.

“I believe that if you have a dream and want to take a step forward that you have to accomplish the tasks before you. He will continue to lead New Jersey,” said Jersey City Councilman Michael Yun.“We want to share the benefits of his leadership with the rest of America,” he added.

FoxNews.com's Karl de Vries contributed to this report.