With six and a half months left until election day, the money war is in full swing. A few days ago, the Obama campaign said that it had raised $53 million in March, bringing its total to just shy of $200 million. Meanwhile, Mitt Romney’s campaign and a Super PAC closely tied to it raised $12.7 million, bringing his total to $87 million.

In announcing the latest fund-raising figure, the Obama campaign boasted that much of it had come from small donors. Some 567,000 people contributed to the reëlection effort last month, the campaign said. More than ninety-seven per cent of the donations were for less than $250, and the average donation was $50.78. Some were as small as five bucks. “This really is how it works,” Jim Messina, Obama’s campaign manager, said in a (http://www.youtube.com/watch?v=YAiCyRKqswQ) that was posted on YouTube. “People building this organization five or ten bucks at a time to take on Mitt Romney.”

Mmm. Up to a point, Jim.

The Obama campaign’s grassroots fund-raising effort is certainly impressive. Heavily based on the Internet, it allows donors to create their own fund-raising pages and uses many of the tricks of online marketing. On Friday, the campaign launched an online raffle, with the prize being a seat at a fund-raising dinner that George Clooney is hosting for Obama at his Los Angeles home, on May 10th. For people who want to try and win the prize, which includes round-trip airfare and accommodation in Los Angeles, the suggested donation is just three dollars each.

Drawing on data from the Obama campaign, some media accounts have suggested that grassroots fund-raising is replacing the traditional technique of soliciting big checks from rich people. A front-page story in Saturday’s Times featured the headline: “Big Donations Drop Sharply for President: Campaign is Relying on Smaller Gifts.” That is certainly what the Obama campaign would like people to think: scrappy Barack, the defender of ordinary Americans, is relying on small donations from waitresses and factory workers to take on big bad Mitt and his fellow-members of the one per cent. But this isn’t the full picture.

Obama has certainly raised a lot more money in small donations than Romney, who has had a hard time attracting any. But soliciting donations from non-wealthy Americans is just part of the President’s fund-raising efforts—and a relatively small part. Even now, his campaign is raising most of the money it will rely on in the election from rich people. The President’s big donors haven’t disappeared for the 2012 campaign. By some measures, there are more of them than ever. You just need to count them properly.

Some accounts focus too narrowly on the fund-raising figures from individual campaigns. Saturday’s story in the Times, for example, said that “about 58 percent of Obama’s total fund-raising during the election has come in checks of less than $200.” That sounds impressive. But it ignores the fact that, these days, most of the money rich people contribute to a candidate doesn’t go to his campaign. In order to comply with campaign-finance laws, it is channelled through allied groups, such as political-action committees (PACs) organized by the two parties, or by outside Super PACs. (Under the Supreme Court’s 2010 Citizens United ruling, the latter groups can raise unlimited contributions from individuals and corporations.)

As is well known, Romney and the Republicans are relying heavily on Super PACs. In March, Restore Our Future, a Super PAC closely allied with Romney, raised $8.7 million, bringing its total to $51.9 million. This figure pales in comparison to the fund-raising efforts of American Crossroads GPS, a Republican Super PAC founded by Karl Rove, which said last week that it has raised $99.8 million. Since Crossroads isn’t obliged to disclose its donors, we don’t know where most of this money came from, but we do know that much of it came in big chunks. In a tax filing last week, the group said that twenty-four donations of over a million dollars have accounted for eighty-seven per cent of its total fund-raising. Two of the donations were for more than ten million dollars.

Obama is also encouraging people to donate to a Super PAC tied to his campaign, Priorities USA Action, but in raising the big bucks he is mainly relying on a more traditional tactic: exclusive dinners where well-heeled Democratic supporters pay $35,800 for the privilege of dining with the President and hearing him talk. That figure is no accident. Under campaign-finance laws, the maximum an individual can give to a candidate is $2,500, and the maximum an individual can give to a PAC legally aligned with a candidate is $5,000. But individuals can give another $30,800 to a national-party committee, in this case, the Democratic National Committee. When the dinner checks for $35,800 come in, the money is split between the Obama campaign and the D.N.C., but the distinction is moot. Practically all of it will be used to help get Obama reëlected.

While the Obama campaign has raised less money so far than it did in 2008—$196 million compared to $235 million—the D.N.C. has raised a lot more: $150 million compared to $69 million. If you combine the two sets of figures, you will find that the broadly defined Obama reëlection campaign has raised $346 million this year, which is more than the $304 million it had raised at this point in 2008. And much of this money has come in large donations.

At the top end, much of Obama’s fund-raising activity is organized by “bundlers,” wealthy individuals who donate the legal maximum of their own money and then put together contributions from their friends, associates, and co-workers. As the Washington Post ’s T. W. Farnam pointed out in an informative story on Saturday, the number of big-money Obama bundlers isn’t declining—it’s increasing. The campaign has published the names of a hundred and seventeen people who have raised at least five hundred thousand dollars. The number of big bundlers has doubled since the start of this year, and it compares with just forty-seven bundlers who raised that amount in 2008.

The list of big-name bundlers was about what you would expect. It was heavy on the media and entertainment industries—Jeffrey Katzenberg, Tyler Perry, Harvey Weinstein. But there were also plenty of rich folks from other walks of life, such as lawyers, industrialists, and real-estate developers. Despite all that has been written about Wall Street turning against Obama, there were also some financiers, including the two hedge-fund managers David Shaw and Blair Effron, and Jon Corzine, the embattled former head of MF Global.

“The lengthening list of top fund-raisers is a sign that bigger donors are coming off the sidelines as the outlines of the race against Romney becomes clear,” Farnam wrote. That sounds about right. Raising money from ordinary Americans is all very well, and the Obama campaign will continue to do it to the best of its ability. But with Democrats and Republicans both aiming to raise upwards of $750 million by the time the election is done, the President will also be busy doing what all of his recent predecessors have done: hitting up rich people for donations. And on the evidence so far, he’s rather better at it than he’s been given credit for.

Photograph by Chip Somodevilla/Getty Images.