Senator Richard Lugar, the chairman of the senate foreign relations committee said the security situation in some cities was a shambles.
The senator added that the administration's plans were sketchy, while Iraqi police forces were not ready to take over.
Asked whether the transfer of power was coming too soon, Mr Lugar said: "It may be, and I think it's probably time to have that debate."
He added: "At this point, I would have thought there would have been a more comprehensive plan."
The senior Democrat on the committee, Joseph Biden, echoed Mr Lugar's concerns.
"We're going to end up with a civil war in Iraq if in fact we decide we can turn this over, including the bulk of the security, to the Iraqis between now and then," Mr Biden said yesterday.
The White House responded by saying it stood by its June 30 deadline, but would keep US forces in Iraq until the country was "free and peaceful".
The remarks came as senior officials at the CIA and state department have conceded that the Sunni triangle in Iraq has become a base from which Islamist jihadists could train and test their cadre.
Officials also admitted in remarks made to the Washington Post that the war on Iraq had widened the constituency for Osama bin Laden's brand of anti-Americanism among Islamist militants.
The insurgency in Iraq had, the sources told the newspaper, created "a new Rolodex of fellow jihadists and people with whom they can work in the [Persian] Gulf in the future".