Carter was previously the deputy Defense secretary, serving from October 2011 to December 2013 under secretaries Hagel and Leon Panetta. Before that, he was in charge of procurement for the Pentagon.
Republican Sen. James Inhofe, the ranking member on the Senate Armed Services Committee, said he's in favor of the nomination. "I support it very strongly. I've known him for a long time. "¦ I can't imagine there'll be significant opposition."
"He would be a great choice," said Democratic Sen. Carl Levin, currently the committee's chairman. Levin and Inhofe said they have heard only news reports of Carter's nomination.
Sen. John McCain, who will likely take over as chairman in January, also said he would support Carter. He said he expects a smooth confirmation process but wants to put Carter through full questioning. Carter is "qualified" for the job, McCain said, but the confirmation hearings will likely center on the administration's strategy against the Islamic State rather than on Carter's background.
Asked if Carter is the right choice to lead the U.S. strategy against ISIS, McCain criticized the president's approach to national security. "He can't. No one can. Because the White House, according to his three predecessors, centers all of their decision-making amongst a handful of people in the White House who only have one thing in common: that they don't know anything about the military."
When he became deputy secretary in 2011, Carter was charged with overseeing military budget cuts, experience that will likely come in handy as the military faces another round of sequestration. He also was responsible for managing the Pentagon's 2.2 million employees. Previously, when he was assistant secretary of Defense for international security policy under President Clinton, Carter played an active role in nuclear arms control issues.
"He's well respected within the defense community, but at the end of the day, it's hard to get somebody to help you implement your strategy when you haven't defined what your strategy is," said Sen. Roy Blunt, R-Mo., a member of the Armed Services Committee. "And that would be his biggest challenge, I would think, before the Armed Services Committee in the Senate."
Sen. Ted Cruz, who has suggested blocking executive nominees over Obama's use of executive action on immigration, said last week that he wouldn't stand in the way of a Defense secretary successor because that position is vital to national security.
Carter has a background in academia in addition to his work in government. He was chair of Harvard's International and Global Affairs faculty and holds a Ph.D. in theoretical physics from Oxford University, where he studied as a Rhodes scholar.
Carter's name rose to the top in a crowded field that included former Defense undersecretary Michele Flournoy, who was previously considered the favorite for the nomination, as well as Homeland Security Secretary Jeh Johnson. Flournoy withdrew her name from consideration last week, and Johnson was no longer being considered as of Tuesday morning, according to CNN.