The State Department on Wednesday said Tuesday’s election results don’t change Secretary of State Hillary Rodham Clinton’s plans to step down.

State Department spokeswoman Victoria Nuland on Wednesday said members of the news media may have “misread” recent remarks in which Mrs. Clinton suggested she might stay longer.

Speculation is surging through foreign policy circles over how quickly the Obama administration will move to nominate a successor, with Sen. John F. Kerry, Massachusetts Democrat, and Susan Rice, the current ambassador to the United Nations, believed to be on the short list.

But the potential downside of picking Ms. Rice or Mr. Kerry — either choice could create thorny political problems for the administration — has some wondering whether the White House might consider capitalizing upon the moment by offering a Cabinet-level olive branch to Republicans.

Names bandied about Wednesday included former Republican Sen. Chuck Hagel, who presently is chairman of President Obama’s Intelligence Advisory Board, and Sen. Richard G. Lugar, Indiana Republican and former chairman of the Senate Foreign Relations Committee, who lost his party’s primary for re-election earlier this year.

“It’s an out-of-the-box suggestion, but it would capture the desire for bipartisanship and that is to ask the outgoing senior senator from Indiana to be secretary of state,” said Karl F. Inderfurth, a senior adviser at the Center for Strategic International Studies.

“I think the administration will look to incorporate centrist Republicans,” added H. Andrew Schwartz, a senior vice president at the center, who said that might mean taking “a close look at Chuck Hagel both for secretary of state and for secretary of defense.”

The challenge of replacing Mrs. Clinton, popular among foreign dignitaries and people in their nations, is likely to prove among the most difficult issue facing the Obama administration going into the second term.

Mr. Kerry, the chairman of the Senate Foreign Relations Committee, appeared to be the administration’s most likely choice. But it now remains to be seen whether the Democratic Party will accept his departure from the Senate.

The Democrats could retain their majority in the Senate even if they lost Mr. Kerry’s seat. But some in the party may still resist, since the subsequent shock-election would create an immediate opening for Massachusetts Republican Sen. Scott P. Brown, who lost his own seat on Tuesday.

Ms. Rice, meanwhile, has faced a rash of criticism from Republicans over statements she made following the Sept. 11 killing of American Ambassador J. Christopher Stephens in Libya. It remains to be seen whether the administration has the stomach for the grueling confirmation hearing she is likely to face if nominated to replace Mrs. Clinton.

More than any political calculation, however, Mr. Schwartz said the White House is likely to weigh the secretary of state nomination very carefully to avoid sacrificing the successes it has achieved in foreign policy over the past four years. That could mean a much slower transition process than State Department officials are suggesting.

“I think the administration has accomplished a lot,” he said. “They’ve gone a long way to restoring America’s dignity internationally and it’s extremely important that there’s a smooth transition.”

“So I don’t think anybody’s going to be in a rush to make that happen.”

Such factors could play into Mr. Lugar’s possible rise on the short list.

“He is obviously a person of great stature and respected by both parties and has established in the past a close relationship with then-Senator Obama,” Mr. Inderfurth said. “They both worked together on the so-called Nunn-Lugar cooperative threat reduction programs. They traveled together.”

While tapping Mr. Lugar would be “quite a statement,” Mr. Inderfurth said the president set such a precedent when he kept Republican-appointed former Defense Secretary Robert M. Gates at the Pentagon well into the administration’s first term.

“Lugar, if you will, is the foreign policy equivalent of the national security specialist Robert Gates,” he said.

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