During an appearance on CBS' Face the Nation, the vice president also said he expects the Democratic-led Congress will eventually relent in its demand that future funding for the Iraq war be tied with a timetable for withdrawal.
"I think the Congress will pass clean legislation," Cheney said. "I don't think that the majority of the Democrats in Congress want to leave America's fighting forces in harm's way without the resources they need to defend themselves."
Congressional leaders have been invited to meet with President Bush at the White House on Wednesday. Both the House and Senate have passed supplemental funding bills for the war that include timetables for withdrawing U.S. troops from Iraq by March 2008. Mr. Bush has vowed to veto such legislation, and Democrats do not have enough votes to override him.
While some Democrats, such as Michigan Sen. Carl Levin, have signaled a desire to send the president a bill he will sign after an initial veto, Senate Majority Leader Harry Reid has said his party will not back down. Cheney said such actions would be "irresponsible," especially after the Senate overwhelmingly confirmed the nomination of Gen. David Petreaus to lead combat operations in Iraq.
When suggested by CBS Evening News chief Washington correspondent Bob Schieffer that a majority of Americans want a timetable for American troop withdrawals from Iraq, as has been voted on in Congress, Cheney said, "Well, there is also a majority that I think would prefer to have us win. And there is a fundamental debate going on here in terms of whether or not our objective in Iraq is to quote 'withdrawal' or whether our objective in Iraq is to complete the mission. And I think a majority of Americans would prefer the latter."
Recent events in Iraq, including a Thursday suicide bomber attack on the Iraqi Parliament building, have not dimmed Cheney's hopes for victory, he said.
"I don't want to underestimate the difficulty of the task, Bob, but just because it's hard doesn't mean we shouldn't do it."
"There is no question it's a very difficult assignment, but we've got a new commander in the field, we've got a good strategy in place, and I think we will soon see positive results," he said.
He said leaving Iraq now would signal U.S. withdrawal from a global war on terror, sending the wrong message to allies such as Pakistan. "Are they going to have any confidence at all that the United States is going to stay and complete its mission?" Cheney said.
In response to Schieffer's suggestion that Cheney's 2005 remark that the Iraq insurgency was in its "last throes" might make some dispute his optimistic take on the war going forward, the vice president suggested his comments lacked hindsight ("We have to respond to questions from the press and we do the best we can with what we know at the time"), but still spoke that progress in Iraq was evident.
"My statement at the time that you referenced was geared specifically to the fact that we just had an election in Iraq where some 12 million people defied the car bombers and the assassins and for the first time participated in a free election," Cheney said. "We had three elections in 2005 in Iraq: We set up a provisional government, then we got a ratification of a brand new constitution, then elections under that constitution of a new government, the government that is in place now. I still think in the broad sweep of history those will have been major turning points in the war in Iraq."
In other current issues, the administration continues to back Attorney General Alberto Gonzales, Cheney said, even as the controversy surrounding the firings of eight U.S. attorneys continues to grow. E-mails released Friday showed that successors for the attorneys were under consideration nearly a year before their firings — an apparent contradiction of Gonzales' testimony before Congress.
"He is a good man," Cheney said of Gonzales. "I have every confidence in him. The president has every confidence in him."
The vice president would not discuss the conviction of Libby on charges of perjury and obstruction of justice as part of the investigation into the leak of former CIA operative Valerie Plame's identity. The case is under appeal.
Cheney called the verdict a "great tragedy" but said he had not talked to Libby since he was found guilty on March 6. "I haven't had occasion to do that," he said.
He also refuted claims by Reid that, amid a hostile Congress and the president's declining approval ratings, he and other members of the administration had become more isolated that Richard Nixon's White House during the Watergate scandal.
"It's a ridiculous notion," Cheney said.