Fallon also accused Iraq's neighbour, Iran, which has been identified by US officials as a source of increasing concern, of fomenting violence beyond its borders and called its behaviour "destabilising and troubling".
Extra US troops
He would oversee Bush's plan to stabilise Iraq, announced this month, which involves the deployment of 21,500 extra US troops.
"I believe the situation in Iraq can be turned around, but time is short," Fallon told the committee, meeting to consider his nomination.
He sounded a note of caution when asked about the prospects of a democratic Iraq emerging from current levels of violence.
"I think that we would probably be wise to temper our expectations here," he said.
"The likelihood that Iraq is suddenly going to turn into something that looks close to what we enjoy here in this country is going to be a long time coming."
Many tens of thousands of Iraqis and more than 3,000 US troops have died since the US-led invasion of Iraq in 2003, with the country in the grip of sectarian violence, an insurgency, Islamist militant attacks and crime.
In the lead-up to and aftermath of the invasion, US officials spoke of creating a new Iraq which could serve as a beacon of democracy for the entire Middle East.
"Going back to 2003, we had hundreds of good ideas of things that we would like to see in Iraq that are more reflective of the kind of society and process that we enjoy here," Fallon said.
"And it seems to me that we probably erred in our assessment of the ability of these people to take on all of these tasks at the same time.
"Maybe we ought to redefine the goals here a bit and do something that's more realistic in terms of getting some progress and then maybe take on the other things later."
Fallon said establishing security and getting progress from Iraq's feuding political leaders should be priorities.
If confirmed by the senate, Fallon would take over central command from Army General John Abizaid, who is retiring.
He would oversee the work of Army General David Petraeus, who is to become the senior US commander in Iraq.
Fallon told the committee that the US should watch Iran very closely.
"Iranian support for terrorism and sectarian violence beyond its borders and its pursuit of nuclear capability is destabilising and troubling," he said.
Fallon said he believed that Iran wanted the ability to prevent the US from operating in the Strait of Hormuz area, a key oil supply route in the Gulf.
But he also said that Iran needed to be able to move freely in the same area to transport its own oil exports.