Host Bob Scheiffer told Sestak that some believe one of the big reasons politics doesn't work is that candidates have to raise so much money and secure the backing of so many interest groups it becomes impossible to compromise.
Sestak, who is backing a bill to move to public financing of campaigns, said that isn't an issue for him.
"At the end of the day, I can look someone in the eye and say 'I appreciate your support but I'm gonna still do what's right,'" said Sestak, invoking his Navy service. "This is payback to this nation."
The White House and Democratic establishment backed Specter over Sestak in the primary, and Schieffer asked if Sestak would ask for President Obama's help in the general election.
Sestak said he welcomes the president's support and would be "honored" if he came to Pennsylvania to campaign with him.
"Yes, I'll stand up to the party if they're wrong and they aren't going the right way for people in Pennsylvania," he said. "But I do believe in Democratic principles."
Sestak said his victory was driven by the fact that people have "lost faith in Washington, D.C." He said his campaign was about demonstrating to people it was about their jobs, not his.
It's about "trying to regain their trust, like in the Navy," he said. "A captain of a ship would always walk around, have captain calls and sit down and listen. At the end of the day, they get a cut of your job. And then they'll follow you if they trust you to do anything. And that's what Washington has to regain."
Shieffer also asked Sestak about the suggestion that, early in the race, the White House had offered him a high-ranking administration job in return for dropping his primary challenge against Specter. Republicans have suggested that any offer may have been illegal and have called for a special prosecutor to investigate.
Sestak again indicated that the offer had been made but added that "anything beyond that just gets into politics."
Earlier in the broadcast, Schieffer asked White House Press Secretary Robert Gibbs about the alleged offer.
"Lawyers in the White House and others have looked into conversations that were had with Congressman Sestak," he said. "And nothing inappropriate happened."
Asked directly if Sestak had been offered a job, Gibbs replied, "I'm not going to get further into what the conversations were. People that have looked into them assure me that they weren't inappropriate in any way."