It was like a mantra when Bill Clinton ran for president in 1992, that we should reward people who “work hard and play by the rules.”

Increasingly, the rap on his wife is that she doesn’t play by the rules.

The New York Times exclusive on Hillary Clinton exclusively using a private email account during her four years as secretary of State—and that this “may have violated federal requirements that officials’ correspondence be retained as part of the agency’s record”—is the latest story to feed that narrative. It follows aggressive reporting by the Washington Post and Wall Street Journal on the Clinton Foundation raising big bucks from foreign governments even while she was in the Obama Cabinet, and in one case violating an agreement with the administration.

So much for the conventional wisdom is that the media are going to roll over for Hillary in the 2016 campaign. She has become a major target for the press, and here’s why.

One, she’s the only game in town on the Democratic side, with no real rival to draw the attention of investigative reporters. Simply put, she’s a big target.

Two, Hillary has a long history of testy relations with the press corps, which hurt her in the 2008 campaign and dates back to her years as first lady. So the coziness factor that many people imagine simply isn’t there.

And finally, while most journalists are more sympathetic to her politics than, say, those of Ted Cruz, Clinton isn’t liberal enough for some in the media, who view her as a Wall Street and foreign policy hawk. They prefer to swoon over Elizabeth Warren and her non-candidacy.

What the email furor and the foundation fundraising mess have in common is that Hillary’s usual media allies aren’t rushing to defend her. Indeed, the New York Times editorial page scolded the Clinton Foundation and called for an end to the buckraking from foreign regimes.

And here’s Lawrence O’Donnell reacting to the e-mail story on his MSNBC show:

“If it’s true that she never used a State Department email address, we have something that, at first read, has no conceivable rational explanation to it that is legitimate.”

Clinton’s use of a private email account emerged because a House committee investigating Benghazi asked for her correspondence. Thus, regardless of what is in those emails, her rejection of a regular government account brings that investigation back into the news.

The Times piece noted that Colin Powell used a personal email account when he ran the State Department, but the rules requiring the use of government accounts were not yet in effect, and it is not clear whether Powell also had an official department email.

The flap also enabled Jeb Bush, who released 250,000 emails from his tenure as Florida governor, to take a Twitter swipe at Clinton over transparency.

Some media folks are using the latest controversy to urge Hillary to quickly get into the race. (The guessing game is all over the map: Politico had reported she would announce her candidacy in April, then reported she would delay until July, and now the Journal says it will be April.)

As an unofficial candidate, says Politico, “she’s already absorbing her share of damaging mid-campaign-style salvos from reporters and Republicans — without actual campaign staff to defend her.”

Instead, Hillaryland “has left the task of defending the former secretary of state — and her family — to a small corps of well-regarded, loyal and badly overstretched aides who have been forced to deal with an avalanche of requests about the foundation, starting with reports that officials solicited millions in donations from foreign governments. Clinton’s personal spokesman Nick Merrill, for example, declined to comment for this story.”

Merrill works hard at fielding inquiries, but his response to the last two controversies has been thin, presumably because he hasn’t been given much to work with. His comment that Hillary had complied with “the letter and spirit of the rules” didn’t do much to blunt the email revelation.

“Clinton's problem isn't a lack of staff. It's a lack of shame about money, personal accountability, and transparency,” says National Journal’s Ron Fournier, questioning whether she should run at all.

But the media’s insistence that Hillary must plunge into the race immediately if not sooner is about their agenda, not hers. The pundits want more access to Hillary, more campaign officials to deal with. They want her in the daily fray because that makes for better copy. They’re frustrated that she’s sitting on the sidelines when they’re all dressed up and ready to cover a two-year campaign.

So they float such various reasons: Her supporters are getting restless. Her donors need more time to raise money. She needs more flacks to deal with the press—as if any array of spinners and spokesmen could have defused the criticism over foreign fundraising and private emails.

On the other side, the sooner that Hillary becomes an official candidate, the sooner she gets pummeled even more and is expected to respond to every hostile criticism and tweet. And, after a quarter century in the public spotlight, the sooner that the public becomes tired of her.   

Either way, Hillary Clinton has to get a whole lot better at playing defense over her series of mistakes. I’d tell her directly, but I don’t have her private email.

Footnote: Times Public Editor Margaret Sullivan fielded complaints from readers who think the headline was too weak: “Hillary Clinton Used Personal Email at State Dept., Possibly Breaking Rules.” The critics say the headline should have been about breaking “laws.”

Says Sullivan: “The Times was cautious in its headline – reasonably so, in my view, though it may have been better to say ‘apparently’ instead of ‘possibly.’

“At any rate, the mere fact of the story, along with its prominent display, argues strongly against The Times being too soft on the former secretary of state.”

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Howard Kurtz is a Fox News analyst and the host of "MediaBuzz" (Sundays 11 a.m. and 5 p.m. ET). He is the author of five books and is based in Washington. Follow him at @HowardKurtz. Click here for more information on Howard Kurtz.