Last Wednesday afternoon, reporters swarmed Sen. Bob Corker in a hallway outside the Senate chamber. The throng was so thick that Capitol police had to move people aside to make room for Corker’s colleagues to pass.

The media crush came because the Tennessee Republican was a key player in the high-stakes multibillion-dollar fight over debit card swipe fees. Corker’s side lost that skirmish on the Senate floor.

But another step the senator took last week may have been more important, both to his future and to that of the broader Republican agenda: He teamed up with Sen. James Webb (D-Va.) to introduce a resolution criticizing the Obama administration for its handling of the military operation in Libya.

“I find it unbelievable that the president would seek the approval of the United Nations and the Arab League for military operations over Libya while sidelining the body that speaks for the American people, not even answering our questions,” Corker said on the Senate floor. “This is not consultation, nor is the president heeding the concerns of his own constituents.”

Corker’s pronouncements on Libya, Afghanistan and other U.S. entanglements abroad are crucial, because although he’s known mostly for his forays into domestic economic policy, he is also the second-ranking Republican on the Foreign Relations Committee. If Republicans do well in November 2012, Corker could even become the panel’s chairman.

The current top Republican, Sen. Richard G. Lugar, is one of his party’s most experienced and best-known voices on foreign policy issues. But he’s being challenged back home in Indiana, facing a tough fight in the 2012 Republican primary. If Lugar loses, Corker could well succeed him. (Because of the Senate GOP’s complicated term-limit rules, Corker could move up in 2013 to the top post even if Lugar is reelected — as long as Republicans remain in the minority.)

Corker’s ascent is far from certain. He is also up for reelection next year, and even if he wins and has the opportunity to move up, Corker could decide to focus his attention elsewhere.

Foreign Relations would be an odd perch, given that Corker is better known for having played key roles in the debates over financial reform, health care and the auto industry bailout. He is known for his willingness to work with Democrats on key issues, a relatively rare trait in the modern Senate.

“The first stage is to be reelected,” Corker said Monday when asked about his committee ambitions. “I’m working on that hard.”

Corker ran his own construction and real estate companies and then served as mayor of Chattanooga before being elected to the Senate in 2006. He acknowledges that he never showed much interest in international issues before joining the Foreign Relations panel, though he does credit a mission trip to Haiti he took in his late 20s with sparking his desire to do public service.

Corker believes he has brought something useful to the Senate committee.

“I think I’ve had an ability to cut through all the diplo-speak . . . and try to focus on something that matters,” he said.

Libya isn’t the only subject on which Corker has criticized the Obama administration.

“What we’re doing in Afghanistan is not sustainable,” he said Monday, complaining of the “nation-building” effort the United States has embarked on. “I think a lot of folks have come around to that conclusion. I’ve been saying that since Day One.”

That outspokenness has caught the eye of some colleagues, including those across the aisle. Webb called Corker “a serious-minded senator who is not afraid to ask hard questions or to confront the prevailing orthodoxy of the so-called foreign policy establishment.”

Corker has earned respect by learning the details of policy issues, and by not being afraid to offer his opinions at internal Republican meetings.

“Some senators are generalists — what we call ‘liberal arts senators,’ ” a Senate GOP leadership aide said. “He has majors. He digs into things.”

Corker has joined Lugar in voicing skepticism about the Libya mission, and he also sided with Lugar (and against most other Republicans) in supporting the START nuclear arms treaty in December. Yet Corker says he hasn’t sought to model himself after Lugar or any other colleague on international issues.

“There isn’t anybody in the Senate today, I would say candidly, that I would say is my role model on Foreign Relations,” he said.

Corker serves on the banking committee as well, and said that panel’s work “has been my wheelhouse.” He also could ask for a seat on the powerful Finance Committee. Yet even if he is instinctively drawn toward economic issues, the top slot on Foreign Relations could be too tempting to pass up.