John Adams called it “the most insignificant office that ever the invention of man contrived.” Thomas Jefferson, who held it next, called it “a station where no effort to render service can avail anything.” Thomas Marshall, who held it a century later, compared the position to being “like a man in a cataleptic state; he cannot speak, he cannot move, he suffers no pain, and yet he is perfectly conscious of everything that is going on about him.” And Walter F. Mondale, who held it only three decades ago, came up with this job description: “Fire hydrant of the nation.”

The vice presidency is no plum assignment. Indeed, Daniel Webster, who ached to become president, wanted nothing of the vice presidency. “I do not propose to be buried,” he said, “before I am dead.”

But if the position of vice president is no prize, then what’s to be said of the position of former vice president?

Ordinarily, not much. Unless the vice president — like Mondale or Albert Gore Jr. — is a plausible presidential candidate, America has traditionally heard almost nothing of its former vice presidents.

Cheney likes to speak out

Now, Dick Cheney, who reshaped the vice presidency during the George W. Bush years, is reshaping the former vice presidency just as dramatically. This winter he has accused President Barack Obama of being weak on terrorism, criticizing the administration for its detention policies, assailing the Obama team for treating terrorist suspects as criminals rather than as enemy combatants, and raising questions about the American commitment to Afghanistan since the end of the Bush administration.

While Bush has remained quiet about the new administration and the threats Americans face at home and abroad, Cheney seems to have reveled in his outspokenness. “I have the great freedom and luxury of speaking out, saying what I want to say, what I believe,” he said on ABC’s “This Week” in early February, two weeks before suffering a mild heart attack, his fifth. “And I have not been discouraged from doing so.”

Cheney’s family has said he will resume his schedule soon, which may include continuing a debate with the current vice president, Joseph R. Biden Jr., who said of his predecessor during an appearance on NBC’s “Meet the Press”: “Dick Cheney’s a fine fellow, but he is not entitled to rewrite history without it being challenged. I don’t know where he has been. Where was he the last four years of the last administration?”

But a broader debate — bigger than whether the Obama administration has grafted much of the Bush administration’s terror policy onto its own — is the role of the vice president and, in Cheney’s case, the former vice president.

The four living former vice presidents who did not advance to the White House took different paths after leaving the lovely home for the seconds-in-command in Northwest Washington.

Mondale joined a law firm and served as ambassador to Japan (though he briefly ran, unsuccessfully, for the Senate in Minnesota after the Democratic Farmer Labor Party’s nominee, Sen. Paul Wellstone, perished in a plane crash late in the campaign season). Dan Quayle went into the investment business. Gore became a global advocate for the environment while tending to some business interests. Cheney remained a pugilist.

Mondale, Quayle differ

“It’s really an individual choice,” Quayle said in an interview last week. “Dick (Cheney) feels he is making a contribution, and he has been able to set the national agenda for a short period of time. Does it bother me? Not at all.”

But it does trouble Mondale. “(Cheney) started going after Obama immediately,” Mondale said in an interview. “There was no honeymoon period. He’s still deeply engaged in discussions about torture policy and foreign surveillance. He wants things consistent with how he had it in the White House, but even (President George W.) Bush grew tired of it.”

Mondale’s concerns grow out of deeper worries about Cheney’s conduct of the vice presidency, an office Mondale began to transform when he became, up until that time, perhaps the most powerful vice president ever, playing a very visible role in the Carter administration.

“He took the model Carter and I established and drove it off the tracks,” said Mondale, 82 years old. “My idea was to help the president with a unique executive perspective. I wasn’t a co-president or prime minister. Cheney became a power unto himself. He had this idea of an invisible, unaccountable secret source of power in the vice president’s office. He managed to be involved in a whole range of intelligence and national security matters. I think it ought to be worrying scholars when something like that happens.”

That was not Quayle’s style, either, nor does Quayle seek outlets to share his views now that he has left Washington and politics for Phoenix and New York City. He does a few fundraisers, but only on his schedule, and he agrees to no commitments more than two weeks in the future. Last week The Washington Post sought him out to write an op-ed piece on the tea-party movement. But otherwise he is staying in the background.

“For me, I was in my early 50s when I left politics and I decided to go do something else,” says Quayle, now 63 and the global chairman of Cerberus, a private equity investment company. “I’m happy in the business world and have had a nice second career. But Dick is in a different place. He’s in Washington, he has easy access to the national media and he has a voice because he has something serious to say on national security, and the Obama administration appears to like to engage him. Those things put him on a national stage that is different from other former vice presidents.”

But Quayle wonders whether the extraordinary departure from customary form might not be Cheney’s at all.

“Here we have the president of the United States engaging a former vice president,” he says. “You have to ask all those geniuses down there why they do that. That’s the remarkable thing here.”

It’s question that really needs to be answered.