Cheney knew what would happen, but chose to invade anyways.
"Q: Do you think the U.S., or U.N. forces, should have moved into Baghdad?
A: No.
Q: Why not?
A: Because if we'd gone to Baghdad we would have been all alone. There wouldn't have been anybody else with us. There would have been a U.S. occupation of Iraq. None of the Arab forces that were willing to fight with us in Kuwait were willing to invade Iraq.
Once you got to Iraq and took it over, took down Saddam Hussein's government, then what are you going to put in its place? That's a very volatile part of the world, and if you take down the central government of Iraq, you could very easily end up seeing pieces of Iraq fly off: part of it, the Syrians would like to have to the west, part of it -- eastern Iraq -- the Iranians would like to claim, they fought over it for eight years. In the north you've got the Kurds, and if the Kurds spin loose and join with the Kurds in Turkey, then you threaten the territorial integrity of Turkey.
It's a quagmire if you go that far and try to take over Iraq.
The other thing was casualties. Everyone was impressed with the fact we were able to do our job with as few casualties as we had. But for the 146 Americans killed in action, and for their families -- it wasn't a cheap war. And the question for the president, in terms of whether or not we went on to Baghdad, took additional casualties in an effort to get Saddam Hussein, was how many additional dead Americans is Saddam worth?
Our judgment was, not very many, and I think we got it right."
Cheney Warns of Iraq Quagmire ... in 1994 | Mother Jones
also
"I think for us to get American military personnel involved in a civil war inside Iraq would literally be a quagmire.
Once we got to Baghdad, what would we do? Who would we put in power? What kind of government would we have? Would it be a Sunni government, a Shi’a government, a Kurdish government? Would it be secular, along the lines of the Ba’ath Party? Would it be fundamentalist Islamic? I do not think the United States wants to have U.S. military forces accept casualties and accept the responsibility of trying to govern Iraq. I think it makes no sense at all."
April 7, 1991 Cheney on ABC news’s This Week
When Dick Cheney told the truth about Iraq - Salon.com