There may be some tension already on Barack Obama’s foreign-policy team.

The president-elect has chosen a few strong personalities in his Cabinet, and this might turn out to bite him where it hurts.

Hillary Clinton and Susan Rice – Obama’s picks for secretary of state and ambassador to the United Nations, respectively – both made trips to the State Department headquarters in Washington Monday for briefings. OK, normal.

What’s not normal is that Rice – according to some officials familiar with the trip who spoke with AP – apparently wants to install her own transition team inside the State Department, though her position will actually be based in New York, near U.N. headquarters. We think Rice may believe she’ll have more power in this post, now that Obama wants to elevate the ambassadorship to a Cabinet position.

But Rice’s request was reportedly denied by the Obama team and Clinton aides.

"Sen. Clinton has great respect for the ambassador-designate and looks forward to working with her," Clinton spokeswoman Kiki McLean told AP.

Obama transition spokeswoman Brooke Anderson added: "Decisions about confirmation and agency review teams were made by the Obama-Biden transition. Given that the U.S. mission to the U.N. is supported by the State Department, it makes perfect sense that our nominee would have an office to use for preparations and meetings there as part of the transition process."

But there may be something more behind this – something that, for Clinton, once again goes back to the Democratic primaries.

Some Clinton aides saw Rice’s early decision to back Obama as a betrayal because she worked in Bill Clinton’s administration. Rice was close with President Clinton’s secretary of state, Madeleine Albright, but the two reportedly split when the elder stateswoman supported Hillary Clinton during the primaries, and Rice not only supported Obama, but went to work for him as a foreign-policy adviser.

But Albright seems to have confidence in the female duo. She said on MSNBC Tuesday morning that both Clinton and Rice will be very involved on issues such as genocide and will work well together.

“I can also assure you that with Susan Rice as ambassador up there and Hillary Clinton in Washington – they’re a great team, along with Secretary [Robert] Gates,” Albright said. 

“I think she’ll do a great job," Albright said of Clinton. "I’ve talked to her a lot and I think she’s very excited and very engaged on all of this but there are huge challenges.

Obama’s national security team will have its hands full — with two hot wars, global economic downturn, terrorism, energy, poverty and other issues plaguing the world. But Obama’s team is “not only impressive but prepared to deal with the challenges," Albright continued. “This team has a huge, huge agenda but a great president-elect and team to do it.”

Clinton also had a dinner date with the woman she is replacing – Condoleezza Rice – at Rice’s Watergate apartment Monday night. President Bush’s secretary of state has gushed over the New York senator. 

We wonder if they talked anything but shop and how to run a federal bureaucracy during their meal of mushroom soup, seabass, wild rice and fruit?