More than 2,800 US soldiers have died in Iraq since the US-led invasion in March 2003, with October one of the bloodiest months to date.
Immediately after taking control of the Senate and the House of Representatives, Democrats, with the support of some Republicans, began pushing the White House for a timetable for withdrawal.
Carl Levin, the incoming chairman of the Senate Armed Services Committee, has said he wants to see a phased pullout of troops beginning in four to six months.
But even as the White House began considering the views of a review board on Iraq policy, Cheney said that pulling US troops out early would be a mistake.
"Some in our country may believe in good faith that retreating from Iraq would make America safer. Recent experience teaches the opposite lesson," Cheney said.
"To get out before the job is done would convince the terrorists, once again, that free nations will change [their] policies, forsake [their] friends and abandon our interests whenever [they] are confronted with violence and blackmail.
"America is going to complete [its] mission, get it done right, and bring our troops home in victory."
Cheney's view was echoed by George Bush, the US president, who on a visit to Vietnam on Friday said that one lesson of the US military defeat there a generation ago was that the United States must be patient in Iraq.
"We'll succeed unless we quit," he said.
Asked whether the US defeat in Vietnam offered lessons, the US president replied: "We tend to want there to be instant success in the world, and the task in Iraq is going to take a while."
Meanwhile, several politicians said that the Pentagon plans to ask Congress for $127 billion for the wars in Iraq and Afghanistan in 2007 in addition to $70 billion already budgeted.
Senator Kent Conrad's office confirmed on Friday that he understood the supplemental budget request would be around $127 billion, while USA Today newspaper reported that Democratic Representative Jim Cooper has said that up to $160 billion might be asked for.