President Bush has nominated U.S. Trade Representative Rob Portman to head the Office of Management and Budget, and picked one of Portman's deputies to fill his current seat.

The president also said Tuesday that he listens to the talk in Washington, D.C., the latest of which has focused intently on an administration shake-up, but one change that will not happen is the replacement of Defense Secretary Donald Rumsfeld.

"I hear the voices and I read the front page and I know the speculation," the president said, answering a reporter's question after his announcement about Portman's nomination. "But I'm the decider and I decide what's best. And what's best is for Don Rumsfeld to remain as the secretary of defense."

Bush added that he has instructed his new chief of staff, Josh Bolten, to "design the White House structure so that it will function, so that he can do his job," and make sure the White House functions properly.

Bush announced his choice for the OMB director's job in a morning Rose Garden event. The Senate will have to confirm Portman and Susan C. Schwab, a deputy USTR who Bush chose to take the top spot at the Office of the U.S. Trade Representative.

"The job of OMB director is a really important post and Rob Portman is the right man to take it on. Rob's talent, expertise and record of success are well known within my administration and on Capitol Hill," Bush said.

Bush said Portman will be a regular part of daily meetings with Bolten, who was the previous OMB director, and will work closely with presidential advisers on developing priorities in the president's budget. He said Schwab's job will be to continue the work of opening trade markets and promoting U.S. priorities in international trade negotiations.

"I look forward to the Senate confirming Rob and Susan and welcoming them to be new members of my Cabinet," Bush said.

A former Republican congressional representative from Ohio, Portman has served in his current position for a year. Elected in a special election in 1993, he was on the House Budget Committee, where he served as a vice chairman, and grew close to the administration while a liaison to the White House during his tenure on Capitol Hill. As head of OMB, one of Portman's priorities will be to push lawmakers to extend Bush's tax cuts that were passed in 2001 and 2003.

Schwab served as a dean at the University of Maryland School of Public Policy and was a legislative director for former Sen. John Danforth. She was the director general of the U.S. and Foreign Commercial Service during President George H.W. Bush's administration.

At the Rose Garden announcement, Portman said he looks forward to working with his former colleagues on Capitol Hill and finding ways to strengthen the economy even more. He credited current successes in the economy in part to the president's push for tax cuts, and said a priority will be to cut spending without raising taxes.

"It's a big job. The Office of Management and Budget touches every spending and policy decision in the federal government," Portman said, adding that he wants to work with Congress to create a workable line-item veto, contain the growth of entitlement spending and reduce earmarks.

Response to Portman's nomination on Capitol Hill was quick. While Republican House leaders who have worked with Portman before said they were pleased, Senate Minority Leader Harry Reid, D-Nev., one of the lawmakers responsible for deciding Portman's confirmation, expressed his obvious displeasure.

"From record trade deficits to record budget deficits, Rob Portman should fit right in at George Bush's OMB," Reid said in a statement.

The move to fill the spot previously held by Bolten was expected and necessary. But more changes in the president's staff are likely to come. Bolten, who took over for Andy Card as White House chief of staff late Friday, told staffers on Monday that if they thought they would leave their posts in the near future, they should do so soon. Trying to ensure a stable staff, Bolten is meeting with each personnel member individually.

"With a new man will come some changes," Bush said of Bolten's arrival at the White House. He said that he will listen to Bolten's suggestions on any staff changes he thinks are appropriate to make.

"I understand this is a matter of high speculation here in Washington. It's the game of musical chairs that people love to follow," Bush said about the possible staff changes. "Of course [Bolten] will bring different recommendations to me as to who should be here and who should not be here."

But the president said he has strong confidence in his Cabinet officials and appreciates "the service they've rendered." He said he does not appreciate the speculation surrounding the departure of Rumsfeld.

"Don Rumsfeld is doing a fine job," Bush said. "A little flicker of gossip starts moving hard and people jump all over it.

"I have strong confidence in Don Rumsfeld," he said.

In a briefing with reporters, Rumsfeld said he has not considered resigning following criticism from a handful of retired generals, some with experience in Iraq, who say Rumsfeld has mishandled the Iraq war and failed to listen to the advice of subordinates. Asked why he has not offered to resign, the way he did following the Abu Ghraib prison scandal, which did not implicate senior Pentagon officials, Rumsfeld replied: "Oh, just call it idiosyncratic."

Bush said that while Washington is fixated on gossip about personnel changes, the administration is dealing with problems such as soaring gasoline prices and the War on Terror.

"I'm concerned about higher gasoline prices," the president said. He said the government has responsibility "to make sure that we watch very carefully and investigate possible price-gouging."

In another personnel change, Jim Towey, head of the White House office of faith-based and community initiatives, resigned to become president of St. Vincent College in Pennsylvania. White House press secretary Scott McClellan said Towey's departure was not related to any White House shake-up.

FOX News' Jim Angle, Wendell Goler and Bret Baier and The Associated Press contributed to this report.