“There are so many incoming missiles that the president is really going to need help no matter how he structures his presidency,” said Joel K. Goldstein, a law professor at St. Louis University and author of “The Modern American Vice Presidency: The Transformation of a Political Institution.” “Yes, we need to know whether the vice president is ready to occupy the highest office, can handle a crisis and be trusted with the nuclear codes. But, equally important, do they have something to offer that will be meaningful in helping the next administration succeed?”

Mr. Goldstein said the ascendancy of the office began with Walter Mondale, who secured a central role as adviser. Jimmy Carter gave him a West Wing office, an autonomous staff and access to all key meetings, perks that have gone to succeeding vice presidents.

Mr. Mondale said in an interview Friday that his role grew from talks he had with Mr. Carter before joining the ticket. He did not want to run any program but to be a freelance adviser with only one client  the president. “I didn’t want to do something someone else is doing, but to help the president on big issues and stay up to speed to be of help when needed,” he said.

Mr. Mondale said that Mr. Cheney took the office that he had modernized and “really went off the rails,” with blowups over wiretapping, torture and the leaking of the name of a C.I.A. employee, Valerie Plame. “This is a real issue that should have been debated last night,” he said.

Mr. Cheney has said that a vice president’s authority derives solely from the Constitution and his relationship with the president. His spokeswoman, Lea Anne Foster, strongly denied that he had overstepped the law or Constitution in the performance of his duties.

Vice presidents after Mr. Mondale were given wider scope than those who came before. President Clinton entrusted Al Gore with the chore of streamlining government and overseeing global warming policy. He also carried a substantial foreign affairs portfolio.

Dan Quayle had a lesser role but kept the West Wing office and met regularly with the first President Bush. He spent much of his time on goodwill missions, raising money and chairing panels on the economy and space.