Cheney acknowledged the situation in Iraq was very unstable but said toppling Saddam Hussein had been the right thing to do. He said he trusted Iraqi Prime Minister Nouri al-Maliki, who he said had demonstrated a willingness to take on lawbreakers regardless of their religious or ethnic affiliations.
"The critics have not suggested a policy — they haven't put anything in place," Cheney said in an occasionally testy interview with a cable news network anchor.
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"All they've recommended is to redeploy or to withdraw our forces. The fact is, we can complete the task in Iraq. We're going to do it. We've got (Lt. Gen. David) Petraeus — Gen. Petraeus taking over. It is a good strategy. It will work. But we have to have the stomach to finish the task."
Cheney bristled when asked to respond to critics who question his daughter Mary's decision to have a baby and raise it with her female partner. "I think you're out of line with that question," replied Cheney, who said he was delighted about having a sixth grandchild.
The vice president said he does not think Sen. Hillary Rodham Clinton of New York would make a very good president "because she's a Democrat."
"I don't agree with her philosophically and from a policy standpoint," he said.
Cheney said he believes Usama bin Laden is alive, but would not speculate about whether he might be hiding in Afghanistan, Pakistan or along their shared border. "I don't want to be that precise," Cheney said.
The vice president said passage of a Senate resolution opposing President Bush's decision to send more troops to Iraq would not change the administration's new strategy in Iraq.
"The Congress has control over the purse strings. They have the right, obviously, if they want, to cut off funding," Cheney said.
"But in terms of this effort, the president has made his decision. We've consulted extensively with them. We'll continue to consult with the Congress. But the fact of the matter is, we need to get the job done."
Asked point-blank if the administration's credibility was at stake, Cheney shot back: "I simply don't accept the premise of your question. I just think it's hogwash."
The vice president said the biggest mistake the United States has made in the war was underestimating the psychological effect the Saddam Hussein regime had on Iraqi citizens.
"I think we underestimated the extent to which 30 years of Saddam's rule had really hammered the population, especially the Shia population, into submissiveness," he said. "It was very hard for them to stand up and take responsibility in part because anybody who had done that in the past had had their heads chopped off."
Complete coverage is available in FOXNews.com's Iraq Center.