Second-term Democratic U.S. President Jackson Evans (Jeff Bridges) must select a new vice president following the sudden death of the current VP. The obvious choice seems to be Virginian Governor Jack Hathaway (William Petersen), who is hailed as a hero after he recently dove into a lake in a failed attempt to save a drowning girl. The president opts not to choose Hathaway, claiming that the administration cannot afford another Chappaquiddick.

The President instead decides that his "swan song" will be helping to break the glass ceiling. He nominates Laine Hanson (Joan Allen), a talented senator from Ohio who is a Republican-turned-Democrat. Standing in her way is Republican Congressman Shelley Runyon (Gary Oldman) of Illinois, who believes she is unqualified for the position, and backs Hathaway for the nod. His investigation in her background turns up an incident where she was apparently photographed participating in a drunken orgy as part of a sorority initiation.

The confirmation hearings begin in Washington, D.C., and Runyon, who chairs the committee, quickly addresses Hanson's alleged sexual imbroglio. Hanson refuses to address the incident, neither confirming nor denying anything, and tries to turn the discussion towards political issues. Anticipating that Hanson would deem her personal past "none of anyone's business," Runyon starts rumors in the media saying that the sexual escapade in college was done in exchange for money and favors, making it prostitution. Meanwhile, a woman testifies in front of the committee saying that Hanson engaged in a relationship with her then-husband prior to their divorce. Though Hanson is not guilty of adultery, her reputation is further tarnished.

Senator Hanson meets with the President and offers to withdraw her name, to save his administration more embarrassment. Despite the wishes of the administration, she refuses to fight back or even address Runyon's charges, arguing that to answer the questions dignifies them being asked in the first place—something she does not believe. The President meets with Runyon, informing him he will not choose Hanson as Vice President. Runyon casually brings forward Governor Hathaway as a replacement. They make an agreement that Runyon will back down on his attacks if the President chooses Hathaway as Vice President. However, the President requests Runyon to make a public statement defending Hathaway.

Hanson, Hathaway and Runyon are all invited to the White House. The president then shocks them by showing a FBI report that proves Hathaway paid the woman to drive off the bridge into the lake. It was part of a plan to increase his approval ratings and become the obvious choice for VP. Hathaway is arrested and Runyon is disgraced because he vouched for Hathaway's integrity just hours earlier. The president meets with Hanson, and she finally tells of what actually happened that night in college. She did indeed arrive at a fraternity house to have sex with two men as part of an initiation, but changed her mind before any sexual acts occurred. The girl in the photo was actually someone else. Though they have the evidence to vindicate Hanson, she explicitly expresses that a statement not be made, even if it will clear her; citing that by doing so will further the idea that it was acceptable to ask the questions in the first place. The president addresses all of Congress and uses Runyon's predicament as a way to gather support for Hanson's nomination.