Barack Obama has just named his pick for the Supreme Court and is still filling out the ranks of his administration. But it’s another casting process, also being conducted in the strictest secrecy, that’s really got them whispering in Washington.

Which five wealthy, connected, ambitious, opinionated, party-going, ­power-brokering women will become the country’s newest “Real Housewives”?

Maybe you thought residents of our nation’s capital were too focused on the economy or North Korea to worry about the casting of a cable reality show. Think again. Ever since the Bravo network announced this week that “The Real Housewives of D.C.” was in development, political blogs have speculated on who’d be tapped for the show. Stories have emerged of stealth screen tests across the city.

“Everybody’s abuzz about it,” says Catherine Merrill Williams, publisher of Washingtonian magazine.

But just how will this franchise, which depends on wealthy women dishing about everything from their finances to plastic surgery to sex, translate to a city where power is defined by access and discretion is paramount?

With difficulty, some say.

“They want people in Washington who get to events where they mix with movers and shakers,” says Williams, whose staff has been consulted by producers looking for the right women. “But it’s unlikely that a working woman here is going to want to do this. In Washington, reputation is everything. Whatever you do is a reflection on your job.”

Besides, adds lobbyist Edwina Rogers, who’s been contacted about joining the cast, “People are so careful about what they say and do here. I suspect that’s why there haven’t been more shows like this about Washington — because people are so private.”

For those whose cable viewing might tend more toward C-SPAN, or maybe just the news channels, a “Real Housewives” primer may be in order. The franchise began in 2006 with “Real Housewives of Orange County.” Versions from New York City, Atlanta and New Jersey followed.

The featured women are always wealthy, have big houses, like to spend money, and like to talk. But there are regional differences.

The New York City show “is not for the faint of heart,” says Andy Cohen, senior vice president of programming and development for Bravo. “They’re either five steps ahead of the rest of us, or they think they are. SO New York.”

The New Jersey show has a more Carmela Soprano feel, with decorating sprees to fill huge, overdone Jersey McMansions. On the Orange County show, “they’re all SO blonde, with SO much hair, real or not,” says Cohen. “They also have huge chests. Never real.”

So how will the doyennes of Washington fit in? Cohen hopes politics will play a role. He’d love to see a Republican woman and a Democrat, each passionate about their views, meeting up at a fancy dinner, where sparks would fly. “Now, that would be fun,” Cohen says.

In Washington the show might get Rogers, a former George W. Bush White House official, Republican strategist and now director of a trade association.

She said she’d been approached but hadn’t yet decided — and hasn’t seen any “Real Housewives” episodes.