Last year's bipartisan Iraq Study Group (ISG) strongly advised against a precipitate withdrawal of US troops.
Such a move would create greater sectarian violence, regional destabilisation, a threat to the global economy and award a propaganda coup to al-Qaeda, it warned.
The war has become hugely unpopular in the US and polls show most Americans want their leaders to come up with some kind of Iraq withdrawal plan.
But a sudden pullout of all troops is not considered feasible on Capitol Hill.
The most precipitous withdrawal plan being put forward in Congress is from Democratic Senator Chris Dodd.
He has proposed legislation that would begin withdrawing troops within a month, pulling them all out by the end of the year.
The New York Times editorial board earlier this year recommended a total pullout that would be completed within as little as six months.
Most advocates of total withdrawal - an idea gathering political momentum - suggest a gradual drawdown, as recommended by the ISG.
The phased pullout option is championed by Democrats and gaining support among centrist Republicans.
In April, Congress backed a Democrat-sponsored proposal for withdrawing the troops, but President George W Bush vetoed it.
The plan from the Democrat-controlled House of Representatives was narrowly supported by the Republican-dominated Senate.
It called for a troop pullout to begin by October this year and be completed by March 2008.
Similar proposals have been tabled by other Democrat Senators, such as Carl Levin, Jack Reed and Russ Feingold.
Democrat candidates in next year's presidential elections have made Iraq a defining issue of their campaign.
Frontrunners Senators Hillary Clinton and Barack Obama and John Edwards all back withdrawal plans of between 12 and 20 months.
Some kind of pullout in the near future seems increasingly likely.
Even US Defence Secretary Robert Gates said recently some troops might be brought home by the end of the year.
STAY THE COURSE
The ISG recommended that with nearly 100 Americans dying every month in Iraq and the US spending $2bn a week on the war, too much blood and treasure was being shed to make staying the course an option any longer.
"Staying until the job is done" is a stance championed by a dwindling number of politicians and commentators.
Most Americans now believe an open-ended US troop commitment will only exacerbate Iraq's problems.
However, President George W Bush this week warned that "to withdraw without getting the job done would be devastating".
He warned Americans that "this enemy would follow us home."
That is a sentiment broadly backed by most Republicans, who have labelled a timetable for withdrawal a "cut and run" or a "surrender date".
The main Republican candidates - Rudy Giuliani, John McCain and Mitt Romney - all want to stay the course - for now.
But tellingly, John McCain, who has been the staunchest cheerleader of Mr Bush's Iraq policy, has seen his support melt away.
His steadfast backing for Mr Bush's security surge, the injection of 30,000 extra US troops into Iraq, has hurt him in the polls, say analysts.
Tensions have emerged between the US and its UK ally recently amid American hawks' concerns that new Prime Minister Gordon Brown could be planning to withdraw the bulk of British troops from southern Iraq in the near future.
The die-hards in the Bush administration are pinning their hopes on the outcome of a progress report by Gen David Petraeus, the senior military commander in Iraq, and Ryan Crocker, the US ambassador, which is to be released to Congress in September.