(CNN) -- President-elect Barack Obama and Sen. John McCain said Monday that Americans are looking for leaders who will come together and "change the bad habits of Washington."
In a joint statement issued after their first meeting since the presidential election, the former rivals said they hoped to work together on challenges such as the financial crisis, creating a new energy economy and protecting the country's security.
"At this defining moment in history, we believe that Americans of all parties want and need their leaders to come together and change the bad habits of Washington so that we can solve the common and urgent challenges of our time," the statement said.
"It is in this spirit that we had a productive conversation today about the need to launch a new era of reform where we take on government waste and bitter partisanship in Washington in order to restore trust in government, and bring back prosperity and opportunity for every hardworking American family," they said.
Obama and McCain met Monday at Obama's transition headquarters in Chicago, Illinois. Watch more on their first post-election meeting »
The two were not expected to talk about any possible Cabinet position for McCain, according to McCain and Obama advisers.
Shortly before the meeting got under way, Obama told reporters he and McCain were going to "have a good conversation about how we can do some work together to fix up the country."
He also said he planned to thank McCain for his service to the country.
Asked whether he would help Obama with his administration, McCain responded, "Obviously."
The meeting comes as Obama is trying to fill out his Cabinet with the most capable people and show he can reach across party lines.
In Obama's first television interview since the election, he told CBS' "60 Minutes" that the global economic crisis provides an opening for the two parties to come together.
"You actually have a consensus among conservative, Republican-leaning economists and liberal, left-leaning economists. And the consensus is this: that we have to do whatever it takes to get this economy moving again, that we're going to have to spend money now to stimulate the economy," Obama said on the program, which aired Sunday.
They were joined Monday by Sen. Lindsey Graham, R-South Carolina, and Obama's new chief of staff, Rahm Emanuel.
Obama last week met with two former rivals for the Democratic nomination -- Sen. Hillary Clinton and Gov. Bill Richardson -- about the secretary of state position in his administration, sources told CNN.
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Ed Rollins, a Republican strategist and CNN contributor, said Obama's meeting with Clinton "makes the Democratic Party very powerful."
"I think it shows Barack Obama's a bigger man than most people in the sense that he's willing to take the person who gave him a real race for his money into his Cabinet," he said.
Obama's transition team has made public some key staff appointments, but no Cabinet positions have been announced.
Republicans have praised the prospect of Clinton becoming secretary of state.
Henry Kissinger, who was secretary of state in the Nixon and Ford administrations, said Clinton would be an "outstanding" selection, Bloomberg News reported.
GOP Sen. Jon Kyl of Arizona told Fox News, "She's got the experience; she's got the temperament for it."
And California Gov. Arnold Schwarzenegger told ABC it would be a "great move."
A new poll suggests most Americans are confident the president-elect will make the right decisions when it comes to picking his top officials.
Forty-three percent of those questioned in a CNN/Opinion Research Corporation survey released Monday morning are very confident that Obama will make the right choices, with 34 percent somewhat confident and only 23 percent not confident.
"Obama is having the kind of honeymoon that no president-elect has had in at least 30 years," said CNN polling director Keating Holland. "It's no surprise that Americans have a positive view of anything Obama might do -- at least until he does something controversial."
Asked which appointment will matter the most to the country's future, 41 percent said the secretary of the treasury; 25 percent said secretary of state; 24 percent, secretary of defense; and 8 percent named the attorney general.
The CNN/Opinion Research Corporation poll was conducted November 6 to 9, with 1,246 adult Americans questioned by telephone. The survey's sampling error is plus or minus 3 percentage points.
Meanwhile, members of Obama's transition team on Monday met with key officials in the State and Defense departments, including Secretary of State Condoleezza Rice.
Rice met with Tom Donilon and Wendy Sherman, Obama's State Department transition team leaders, and promised a smooth hand-over, according to State Department deputy spokesman Robert Wood.
In the half-hour meeting, held at Rice's request, Rice "expressed her desire to work closely with the team on a smooth and professional transition," Wood said.
Obama's Defense Department transition team leaders, John White and Michele Flournoy, made office calls to four senior officials and requested more meetings for later this week, senior Pentagon officials said.
The transition team over the weekend announced several White House appointments.
Peter Rouse, Obama's chief of staff in his Senate office, will serve as a senior adviser to the president. Watch more on the Obama transition picks »
Mona Sutphen will serve as a deputy chief of staff. Sutphen is a member of the transition team staff and has been managing director of Stonebridge International LLC, an international strategic consulting firm based in Washington.
Jim Messina was also named a deputy chief of staff. Messina is currently the director of personnel for the president-elect's transition team. He served as a national chief of staff for Obama's presidential campaign.
Also, a longtime friend of the Obamas, Valerie Jarrett, was officially named Saturday as a senior adviser to the incoming president.
Obama, in a statement released Saturday morning by his transition staff, announced that Jarrett will serve as senior adviser and assistant to the president for intergovernmental relations and public liaison.
Jarrett is currently co-chair of Obama's transition team and was senior adviser for his presidential campaign.
CNN's Suzanne Malveaux, Paul Steinhauser, Elise Labott and Mike Mount contributed to this report.