The comments contradict reports out of Baghdad that a 27-point withdrawal plan had been approved by the two sides.
Bush is vacationing at his ranch in Texas.
The deal being discussed by U.S. and Iraqi negotiators sets a course for American combat troops to pull out of major Iraqi cities by next June, with a broader exit two years later from the long and costly war that began in March 2003.
The dates could be adjusted if security and political progress in Iraq deteriorate.
There are about 140,000 U.S. forces in Iraq, according to United States Central Command, and more than 4,100 American troops have been killed there.
Johndroe would not discuss specifics of the plan being negotiated, including the dates when U.S. troops might begin to leave.
Increased security in Iraq, which the Bush administration said is due to the so-called surge of U.S. forces more than a year ago, created the conditions for the troop withdrawal negotiations to take place, Johndroe said.
The talks take place as Sens. John McCain and Barack Obama regularly trade shots over progress in Iraq and argue over who is better suited to be commander in chief when Bush leaves office in January.
Obama, the Democratic nominee in waiting, wants all U.S. forces out of Iraq within 16 months of his taking office, saying they are needed in Afghanistan. Violence in Afghanistan and neighboring Pakistan has increased due to a resurgent Taliban and political instability in Pakistan.
Obama opposed the U.S. invasion of Iraq. And he's said the surge of troops has not led to the political reconciliation needed to ensure the country will remain secure once all U.S. troops are gone.
McCain, the Republican candidate, supported the president's January 2007 decision to add 30,000 U.S. troops in Iraq. Those additional troops have returned home.
McCain has said the security situation in Iraq should dictate any pullout schedule. And he's criticized Obama for not only opposing the troop surge but trying to block the funding that would have allowed the increase.