Cheney said on Tuesday he believes the power of the presidency has indeed contracted since the Vietnam and Watergate era.
He was talking to reporters aboard his government plane as he flew from Islamabad, Pakistan, where he visited quake-hit areas in Kashmir, to Muscat, Oman, on an overseas mission.
Cheney said he believes the American people support President George W Bush's terror-fighting strategy.
"If there's a backlash pending" because of reports of National Security Agency surveillance of calls originating within the United States, he said, "I think the backlash is going to be against those who are suggesting somehow that we shouldn't take these steps to defend the country".
He added: "It's not an accident that we haven't been hit in four years."
Cheney was speaking amid a burgeoning controversy at home over Bush's acknowledgment of a four-year-old administration program to eavesdrop - without court-approved warrants - on international calls and e-mails of Americans and others inside the US with suspected ties to al-Qaida.
Some Democrats have said they never approved the domestic wiretapping programme, undermining suggestions by the US president and his senior advisers that the plan was fully vetted in a series of congressional briefings.
Jay Rockefeller, the Senate intelligence committee's top Democrat, said in a handwritten letter to Dick Cheney, the vice-president, in July 2003: "I feel unable to fully evaluate, much less endorse, these activities.
"As you know, I am neither a technician nor an attorney."
Cheney was in Pakistan on a one-
day trip to vist quake-hit areas
Rockefeller is among a small group of congressional leaders who have received briefings on the administration's four-year-old programme to eavesdropping.
The government would still seek court approval to snoop on purely domestic communications, such as calls between New York and Los Angeles.
Some legal experts described the programme as groundbreaking.
And until the highly classified programme was disclosed last week, those in Congress with concerns about having the National Security Agency spy on Americans raised them only privately.
Bush, accused of acting above the law, issued on Monday a forceful defence of the programme he first authorised shortly after the attacks of 11 September 2001.
Despite the defence, there was a growing storm of criticism in Congress and calls for investigations from Democrats and Republicans alike.
"I feel unable to fully evaluate, much less endorse, these activities"
Senator Jay Rockefeller,
Senate intelligence committee's top Democrat
Until the past several days, the White House had informed only Congress' top political and intelligence committee leadership about the programme that Bush has reauthorised more than three dozen times.
The spying uproar was the latest controversy about Bush's handling of the "war on terror".
It follows allegations of secret prisons in Eastern Europe and of torture and other mistreatment of detainees, and an American toll in Iraq that has exceeded 2150.