A new book, “The Obamas,” by New York Times reporter Jodi Kantor, reportedly sheds light on the first lady's tense relationships with several White House aides and her difficulties in defining her role in the early days of her husband’s administration.

But here is what I think will stick:

It was the tea party the Obamas just couldn’t resist.

A White House “Alice in Wonderland” costume ball — put on by Johnny Depp and Hollywood director Tim Burton — proved to be a Mad-as-a-Hatter idea that was never made public for fear of a political backlash during hard economic times, according to a new tell-all….

The book reveals how any official announcement of the glittering affair — coming at a time when Tea Party activists and voters furious over the lagging economy, 10-percent unemployment rate, bank bailouts and Obama’s health-care plan were staging protests — quickly vanished down the rabbit hole.

“White House officials were so nervous about how a splashy, Hollywood-esque party would look to jobless Americans — or their representatives in Congress, who would soon vote on health care — that the event was not discussed publicly and Burton’s and Depp’s contributions went unacknowledged,” the book says.

However, the White House made certain that more humble Halloween festivities earlier that day — for thousands of Washington-area schoolkids — were well reported by the press corps….

The State Dining Room had also been transformed into a secretive White House Wonderland.

Tim Burton decorated it “in his signature creepy-comic style. His film version was about to be released, and he had turned the room into the Mad Hatter’s tea party, with a long table set with antique-looking linens, enormous stuffed animals in chairs, and tiered serving plates with treats like bone-shaped meringue cookies,” reports the book, which The Post purchased at a Manhattan bookstore.

“Fruit punch was served in blood vials at the bar. Burton’s own Mad Hatter, the actor Johnny Depp, presided over the scene in full costume, standing up on a table to welcome everyone in character.”

First off, I am wondering how on earth the eagle-eyed White House press corps missed this. The White House is supposed to be a fishbowl, right! Some fishbowl!

What is also hard to understand is how anyone could want to indulge in this kind of slightly decadent party badly enough to throw caution to the winds: It does look bad.

White Houses have had to worry about image before, but this party really does seem to portray a first couple who don’t care to share any part of the vicissitudes faced by normal Americans in these trying times.

The other really shocking incident features former press secretary Robert Gibbs becoming so “enraged” with Mrs. Obama that hecursed her out in a staff meeting.” No excuse for this, Mr. Gibbs. (White House Dossier pursues another angle on this story.)

It must be hard at times to live in the White House, but this book apparently shows a first lady who “bristled” at having too many engagements, is reluctant to do regular duties associated with the role of first lady (such as hosting the annual luncheon for Congressional spouses), and tries to “wriggle” out of ceremonial events.

The stories on the new Kantor book remind me that I’ve long wanted to do a piece with a working title something like this: “First Lady: Get Real—It’s a Great Gig.”  It would refute the feminist notion that this is an awful job because it requires the first lady to hide her personality and play a secondary role. Americans love strong women–just ask Eleanor Roosevelt and many others who did the job with grace, gusto, and good will before the feminist press convinced us it is such living hell!

Just once, I’d love to hear more about what a great privilege and honor, not a burden, it is to serve the country in this capacity. Gladly serving is the flip side of having parties with fruit drinks in blood vials and Hollywood stars in the State Dining Room during a recession.