For someone so famously garrulous, Joe Biden has been remarkably quiet since assuming the vice-presidency in January. That, however, has not stopped his Republican enemies from seizing upon one remark this week as evidence that he is “a blowhard” – a pompous windbag – or even a liar.

In a rare appearance on one of the TV talk shows where he used to be a fixture, Mr Biden sought to rebut claims from his predecessor, Dick Cheney, that America was less safe from terror attack than it was under George Bush.

He told CNN: “I remember President Bush saying to me one time in the Oval Office, ‘Well, Joe,’ he said, ‘I’m a leader’. And I said, ‘Mr President, turn around and look behind you. No one is following’.”

Karl Rove responded: “It didn’t happen . . . it’s a made-up, fictional world. He ought to get out of it and get back to reality.” Speaking on Fox News, the Republican strategist added: “I hate to say this, but he’s a serial exaggerator. If I was being unkind I would say liar.”

Although Mr Biden’s spokesman has issued a statement insisting that he stands by his remarks, the row has reinforced an impression in some quarters that the Vice-President’s tongue is dangerous when let loose.

Yesterday he was back home in Wilmington, Delaware, and had no events scheduled. On Thursday, after Mr Biden read out prepared remarks about extra childcare money, aides swiftly shut down efforts by reporters to ask him questions. “This way guys, out that door,” shouted one, as Mr Biden opened his mouth.

Such a low profile, particularly compared with the stellar arc being cut by President Obama over much of the world, is very deliberate in a White House where message discipline is so highly prized.

On a few occasions Mr Obama has gently admonished his deputy. When Mr Biden joked about Chief Justice John Roberts’s botched delivery of the inaugural oath, the President could be seen squeezing his arm to rein him back. A campaign slip in which Mr Biden suggested that the new Administration would face an early test of its security credentials caused Mr Obama to say: “Sometimes, Joe engages in rhetorical flourishes.”

None of this, however, diminishes the value of the 66-year-old Mr Biden’s experience. His most visible role is to act, in the President’s words, as “sheriff” – preventing wasteful spending of the economic stimulus package, or tapping into his working-class roots to lead a task force on helping poorer families.

The 36 years he spent on Capitol Hill – during much of which he was on the Senate Foreign Relations Committee – means that the Vice-President has sometimes been used as a congressional arm-twister to secure support in crucial votes. He still sees his old colleagues almost daily, often at the Senate gym.

Mr Biden’s greatest influence, however, is wielded behind the scenes. On some days he is with Mr Obama for as long as five hours participating in economic and intelligence briefings as well as any number of other meetings.

His advice is understood to have been decisive in the new strategy for Afghanistan and Pakistan, where he counselled a cautious approach.

On other occasions, he plays the role of devil’s advocate including, it is said, making unsuccessful attempts to get healthcare reform dropped from this year’s budget. “Joe is very good about sometimes articulating what’s on other people’s minds,” Mr Obama said. “Joe, in that sense, can help stir the pot.”

He is not seeking to build up his own power base within the Administration as Mr Cheney did, merely a guarantee that his voice will be heard (at least in private). As Mr Biden himself has stated, his condition for taking the job was that on “every critical decision – economic and political as well as foreign policy – I’ll get to be in the room”.

Mr Biden and Mr Obama have a weekly one-on-one lunch in the Oval Office. The President chooses what to eat, perhaps because of the Vice-President’s habit of inserting a foot into his mouth.

Gems and gaffes

March 2009 “Gimme a f***ing break.” To a former Senate colleague who referred to him as “Mr Vice-President”

September 2008 “Hillary Clinton is as qualified or more qualified than I am to be vice-president of the United States of America.” He was in the running to be vice-president at the time

September 2008 “If you want to know where al-Qaeda lives, you want to know where bin Laden is, come back to Afghanistan with me, come back to the area where my helicopter was forced down, with a three-star general and three senators at 10,500ft in the middle of those mountains. I can tell you where they are.” It later emerged his helicopter had landed because of bad weather

September 2008 “Stand up, Chuck, let ’em see ya.” To Missouri state Senator Chuck Graham, who is in a wheelchair

September 2008 “Look, John’s last-minute economic plan does nothing to tackle the No 1 job facing the middle class, and it happens to be, as Barack says, a three-letter word: jobs. JOBS, jobs.” On John McCain’s economic policy

October 2008 “I mean, you got the first mainstream African-American who is articulate and bright and clean and a nice-looking guy. I mean, that’s a storybook, man.” On Barack Obama, at the start of the election campaign

Times Recommends

• Should Knox’s trial even have reached the courtroom?
• 'Was it real?' The US bailout nightmare
• Iranian opposition plays the long game