"We may be able to do more with less," said Dana Perino, a White House spokeswoman, in a preview of the president's 18-minute address.
"We've got a long way to go. It's very hard. We're realistic about it."
Perino also denounced as "an outrage" the bombing that killed a Iraqi Sunni tribal leader, Sattar Abu Risha, who worked with the US in a campaign against al-Qaeda in the province of Anbar.
Bush is to embrace Petraeus' recommendation to gradually withdraw up to 30,000 of the 169,000 troops currently in Iraq, bringing US forces down to what it was before he ordered a buildup in January.
"Had the US foreign policy makers read history, they would not get involved in any war after Vietnam"
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He will deliver his address after two days of congressional testimony this week by Petraeus and Ryan Crocker, the US ambassador to Iraq.
Democrats in control of the US congress were largely unconvinced by Petraeus' accounts of progress in Iraq and some of Bush's fellow Republicans have also voiced doubts over his strategy.
Democrats say that the Pentagon believes that the "surge" of forces in Iraq this year faces a time limit because of the risk of overstretching the US military.
Hours before the speech, Harry Reid, the Senate Democratic majority leader released a statement noting that Osama bin Laden was still at large 2,193 days after the September 11 attacks.
"Yet each day our valiant men and women are put in harm's way in Iraq policing a civil war.
"Six years after 9/11, it's time for us to put our eye back on the ball," the statement said.
Democrats have said they would launch a new attempt in the senate next week to change the role of US forces in Iraq through legislation tied to a defence spending bill.