Pentagon sources told the newspaper the debate is getting more intense in the run-up to next month's report to Congress by Gen. David Petraeus, the top commander in Iraq.
Most of the 160,000 U.S. soldiers are now serving 15 months in Iraq and get a year or less at home.
In a video briefing Friday, Maj. Gen. Rick Lynch, commander of the Third Infantry Division in Iraq, warned against cutting back U.S. troops.
"What would happen is the enemy would come back," Lynch told reporters. "He’d start building the bombs again, he’d start attacking the locals again, he'd start exporting that violence to Baghdad. We would take a giant step backward."