It would be a tough sell in any office: Hey boss, between that very important meeting and Monday’s very important vote, would you mind getting roasted on a mock news show?

But that’s pretty much what happens when a press secretary on Capitol Hill has to convince his boss to appear on “Better Know a District,” the popular recurring segment on Comedy Central’s “The Colbert Report.”

Somehow it’s worked. So far the “434-part” series has logged more than 80 installments — and more are on the way. Last Friday, Rep. Marcia Fudge (D-Ohio) was spotted with the show’s host, comedian Stephen Colbert, in the Cannon House Office Building. Team Fudge confirmed that the congresswoman had been officially Colbert-ed but declined to provide more details.

Producers at “The Colbert Report” ask members’ offices to remain mum on the two-hour taping’s particulars, but on Friday a serendipitously placed staffer managed to catch Colbert on film. Decked out in full fencing regalia (jacket, mask and sword) Colbert looks directly into a camera and says, “I’m now a proud member of the Congressional Black Caucus.” We’ll have to wait six to eight weeks for the context.

The one thing we do know for sure is that getting members of Congress to go quip-for-quip with a comedian is never an easy task.

“A lot of people see it as being potentially dangerous,” said Paul Kincaid, the communications director for Rep. Tony Cárdenas (D-Calif.). “You just have to realize you’re not a comedian and he is.” Kincaid’s advice has been road tested. He’s gotten two members on the show — his current boss and his former boss — former Rep. Russ Carnahan (D-Mo.).

So why even bother with the scheduling and the nerves? For some members a “Better Know a District” appearance can slingshot them across the recognition line that separates “Representative What’s Her Name” from “Hey, I saw you on Colbert!”

The trick, if there is one, said Kincaid and other press secretaries we interviewed, is to understand the format. Colbert plays the fool and the politician plays him or herself. The cardinal rule? Don’t try to be funny.

“There’s never going to be a point in time when Stephen Colbert comes in and tries to pass laws, so it’s probably a bad idea for you to go on his show and try to tell jokes,” Kincaid explained.

Even with that cut-and-dry code of conduct some members prefer to steer clear of Comedy Central altogether.

“I said no because I want to be taken seriously,” explained Rep. Gwen Moore (D-Wis.), who was so opposed to appearing on a comedy show that she wrote a poem about it. It’s called “Ode To Dr. Colbert.”

Do I dare be interviewed by Dr. Colbert who may lure me into his supercilious Snare?
Should I Go? Or Not Go on his show?  Does this make Sense? Or will He make Me the butt of “his” jokes at my expense?

In the end the congresswoman decided, “If I dare step into Colbert’s lair, casting aside all caution and care — then I’ll march to my fate boldly and do it with flair!”

Moore’s installment, which aired May 15, 2013, was one of the longest in the series, clocking in at more than 12 minutes and two segments. In it Colbert asks if Moore, the first African American woman to represent her district, got the job because of Affirmative Action. The congresswoman doesn’t skip a beat when answering “absolutely not” and then admits to being “openly black.”

But no matter how seasoned or unflappable a politician, “Better Know a District” is not for everyone.

One press secretary said that for members who have “stuff in their past politically or just in general that they don’t want to discuss, it’s probably a bad idea to go on.”

In addition to their own “opposition research,” Colbert’s producers ask for a background packet, an updated biography and more personal details (Fudge took fencing lessons in high school, hence Colbert’s get-up on Friday).

Meanwhile back on the Hill, most members prepare by simply watching the show. “If you spend too much time thinking,”  Moore said, “then you can get caught up. You just have to be yourself and relax.”

Prepping, of course, makes sense. But it doesn’t always pan out.

Before sitting down with Colbert, Moore refreshed her memory on Wisconsin’s state bird and its state beverage (the American robin and milk for those playing at home), but Colbert was more interested in doing an impromptu poetry slam. Unfortunately, none of that made it on air.

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