Stephen Meyers (Ryan Gosling) is the junior campaign manager for Mike Morris, Governor of Pennsylvania and a Democratic presidential candidate, competing against Arkansas Senator Ted Pullman in the Democratic primary. Both campaigns are attempting to secure the endorsement of North Carolina Democratic Senator Franklin Thompson (Jeffrey Wright), who controls 356 convention delegates, enough to clinch the nomination for either candidate. After a debate at Miami University, Meyers is asked by Pullman's campaign manager, Tom Duffy (Paul Giamatti), to meet in secret. Meyers calls his boss, senior campaign manager Paul Zara (Philip Seymour Hoffman), who doesn't answer. Meyers decides to meet Duffy, who offers Meyers a position in Pullman's campaign, an offer Meyers refuses. Zara calls Meyers back and asks what was important, but Meyers says it was nothing to worry about. Meanwhile, Meyers starts a sexual relationship with Molly Stearns (Evan Rachel Wood), an attractive intern for Morris's campaign and daughter of Jack Stearns, the chairman of the Democratic National Committee.
Meyers admits to an angry Zara that he met with Duffy, and that Duffy said his candidate will offer Thompson the position of Secretary of State, guaranteeing Pullman's victory. Zara and Meyers discuss the matter with Morris, saying they must make the same offer to Thompson to secure his endorsement and his delegates' votes. Morris refuses on principle, as he thoroughly disagrees with Thompson and his policies, and wants a "clean" campaign without such deals.
Late one night when Molly is sleeping, Meyers discovers that Morris is trying to call her after he picks up her phone by mistake. Meyers finds out that Molly and Morris had a brief sexual liaison at a campaign stop in Iowa several weeks previously, and Molly is now pregnant by the Governor, which will cause a scandal. Molly needs $900 for an abortion, but cannot tell her father because their family are Catholics. Meyers helps her with money but warns her not to tell anybody. Meyers also fires Molly from the campaign to make the problem go away. Ida Horowicz (Marisa Tomei), a reporter for the New York Times, reveals to Meyers that an anonymous source leaked his encounter with Duffy to her. She also knows the Morris campaign has talked to Thompson. She says she will publish the Duffy meet unless Meyers gives her all of the details about the Thompson meeting.
Meyers comes to Zara for help, believing the story would damage him, Zara, and the campaign. Zara reveals that he leaked the meeting to Ida with Morris's approval in order to force Meyers into resigning from the campaign, stating that he did this because Meyers was disloyal for meeting with Duffy. Zara makes it clear that he holds no personal animosity against Meyers and values him, but cannot trust him any more. An angry and desperate Meyers then offers his services to Duffy, who admits he only met with Meyers to influence his opponent's operation under the likelihood that either Meyers would leave Morris and come to work for him or Meyers would tell Zara, and Zara would fire him. Either way, Duffy would win.
Duffy apologizes for using him, saying that he also wanted to help Meyers, and advises him to quit politics and the campaign before he becomes a cynic like him. Meyers offers to sell out Morris completely but Duffy declines, thinking that Meyers cannot hurt him and he has Thompson wrapped up. Meyers takes her to the abortion clinic and then callously abandons her there with an unfulfilled promise to come back when it's over. Alone in a hotel room, and having been equipped with pills from the clinic, she dies from overdose. Meyers comes on the death scene and sneaks Molly's phone from the bed into his pocket.
Unbeknownst to the Morris campaign, he meets with Thompson to arrange for Thompson's delegates in exchange for a spot on the Morris ticket. It is clear that Thompson prefers Morris over Pullman so all Meyers has done is get Thompson to commit if he is offered the post with Morris. Meyers meets Morris in a dark bar, telling him he will expose the affair with Molly if Morris does not accept his demands: fire Zara, place Meyers in charge of the campaign, and offer Thompson the role of Vice President. Morris coldly says that there is no proof of the affair, but Meyers claims to have a suicide note found in Molly's room. Morris relents, clearly giving up what is left of his personal integrity, and meets Meyers's demands. Zara takes his firing philosophically and is still positive with the press about Morris.
Zara talks to Meyers at Molly's funeral and is amicable, letting Meyers know that he knows Meyers must have had something big on Morris to get him to fire Zara and hire him. Zara has options and states that he is taking a million dollar a year job at a consulting firm, for him basically a retirement from politics. Later, Thompson's endorsement makes Morris the de facto nominee despite losing the Democratic Party's Ohio primary election. Duffy, who put Meyers's back against the wall and who rejected Meyers's offer of dirt against Morris, is seen trying to put up a good face in what is now obviously going to be a defeat for his candidate.
Now senior campaign manager, Meyers is on the way to a remote TV interview with John King, when Ida ambushes him and says her next story will be about how Meyers delivered Thompson and his delegates and got his promotion. Meyers reacts by having security bar her from coming any further. Meyers takes his seat for the interview, just as Morris finishes a speech about how 'integrity and dignity' matter, and is asked for insight as to how the events surrounding the primary unfolded.

Question: What did Tom Duffy offer Stephen Meyers in their secret meeting?
Answer: A position in Ted Pullman's campaign.
Alternative answer: A job with the Pullman campain