"This is a fishing expedition," attorney John Kester said during nearly three hours of argument in U.S. District Court.
Lawyers for Cheney, Karl Rove and two others belittled Plame's suit, saying it should be thrown out of court.
The former CIA officer contends the Bush administration violated her constitutional rights by leaking her identity to reporters in 2003.
Her lawsuit is "principally based on a desire for publicity and book deals," said Michael Waldman, representing former State Department official Richard Armitage.
The case is "about egregious conduct by defendants that ruined a woman's career," countered Plame's attorney, Erwin Chemerinsky.
Plame is demanding compensation from Cheney and his former chief of staff I. Lewis "Scooter" Libby, White House political adviser Rove and Armitage.
Plame's lawyers say the case could reveal more about the inner workings of the Bush White House than surfaced during Libby's monthlong perjury trial, but Thursday's arguments focused on technical matters of law.
Plame and her husband, former Ambassador Joseph Wilson, say the administration violated their free speech, due process and privacy rights.
To succeed, their lawyers must show that Cheney and the other defendants are not immune from such suits because they clearly violated the Constitution.
The Justice Department has asked a judge to drop an invasion of privacy count because government officials cannot be sued personally for such claims when acting in their official capacity.
Several administration officials, including Armitage and Rove, disclosed Plame's identity to reporters in 2003 after Wilson began criticizing prewar intelligence on Iraq.
Nobody was charged with the leak, which would have been a crime only if someone knowingly gave our information about someone covered by a specific law protecting the identities of covert agents.
Libby was convicted in March of obstructing the leak investigation and lying about how he learned about Plame.
Libby is to be sentenced June 5.