Troop surge
Some, such as then Speaker of the House Nancy Pelosi, have credited the Iranian government for all or part of the reduction in violence. Pelosi stated in May 2008 that "some of the success of the surge is that the goodwill of the Iranians-they decided in Basra when the fighting would end, they negotiated that cessation of hostilities-the Iranians." Cockburn has also stated that the Iranians played the major role.
Other commentators have pointed to the Sunni Awakening (which started in 2005) as the most important reason for the decline in Iraqi violence. David Kilcullen, General Petraeus's counterinsurgency and troop surge adviser, believes that "the tribal revolt was arguably the most significant change in the Iraqi operating environment in several years."
One article mentions that "Currently, the dominant U.S presence in Iraq allows the rest of the world to avoid responsibility for stability in and around Iraq even as everyone realizes the stakes involved". In addition "A plan to draw down U.S forces would therefore contribute to the success of a larger diplomatic strategy, prompting Middle Eastern states, European governments, and the UN to be more constructive and proactive in working to salvage stability in the Persian Gulf"
On April 20, 2007, four months after the surge went into effect, Senator Harry Reid made a statement on the floor of the US Senate that the US had already lost the war in Iraq and that the surge would accomplish nothing, stating "I believe myself that the secretary of state, secretary of defense and – you have to make your own decisions as to what the president knows – (know) this war is lost and the surge is not accomplishing anything as indicated by the extreme violence in Iraq yesterday."
Congressional Democrats believed military progress has been made in Iraq but that the political progress that President Bush gave as the primary reason for the surge has not occurred. They continued to call for a withdrawal of American troops. In February 2008, Speaker of the House Nancy Pelosi told reporters that "God knows, anytime our military men and women go into a military exercise, we want them to succeed, and they did. The politics did not follow. So they can paint whatever picture they want on it; the goal has not been accomplished. The tragedies, the casualties continue. We are going in the wrong direction in Iraq." Presidential candidate Hillary Clinton, having already voted to support Petraeus, now stated on Fox News Sunday that month that "the so-called surge was designed to give the Iraqi government the space and time to make the tough decisions that only the Iraqis can make for themselves. ... And I think that putting forward a very clear objective of beginning to withdraw our troops is the best way to get the Iraqis to take responsibility."

Public opinion: An early February 2008 Gallup Poll found that 43% of Americans thought the troop increase was "making the situation there better". A CNN poll conducted during the same period found that 52% thought that US forces were "making progress in improving conditions in Iraq and bringing an end to the violence in that country" while 45% disagree. A poll released by the Pew Research Center on the same day found that 48% of those polled believed the war to be going well, up from 30% a year earlier, with a similar number supporting keeping troops in Iraq "until the situation has stabilized". A majority still believed the war to be a wrong decision in the first place.  A commentary on the poll by National Public Radio called some of its results a "sign that the troop surge is being seen as successful." Nonetheless, an Opinion Research Corporation poll conducted in June 2008 found that 68% of Americans were opposed to the war in Iraq and that 64% of Americans wanted to see the next President remove most troops from Iraq within a few months of taking office. A summer 2008 CBS News poll found that 46% thought it improved the situation in Iraq while 11% thought it made it worse and 32% thought it had no impact.
A March 2008 poll of Iraq found that 42% of Iraqis called attacks on US forces acceptable and that only 4% of Iraqis believed that US forces were responsible for the drop in violence. The poll also found that 61% believed that the presence of US troops in Iraq was actually worsening the security situation. In July 2008, Iraqi Prime Minister Nuri Al-Maliki and Iraqi National security advisor Muwaffaq Al-Rubaie both sought a timetable for the withdrawal of foreign troops.
A CNN/Opinion Research Corporation Poll conducted September 1–2, 2010, revisited this question "As you may know, the US. sent 20,000 combat troops to Iraq in 2007 in what was called a surge. Based on what you have read or heard, do you think that surge of U.S. troops to Iraq was a success or a failure?"  60% responded as success, 33% failure and 7% depends or unsure.

See also: 

Further reading: Petersen, Roger D. (2024). Death, Dominance, and State-Building: The US in Iraq and the Future of American Military Intervention. Oxford University Press.

References: 

External links: "Neocons Put on a Surge-Stravaganza," CommonDreams.org News Center, September 8, 2007.
AEI Surge Study
Blythe, Jr., Wilson C. "III Corps During the Surge: A Study in Operational Art." Army Press Online Journal (13 January 2017).  Blythe-III Corps during the Surge
Hope for Iraq's Meanest City, City Journal, Spring 2008
Iraq: Violence is down – but not because of America's 'surge', by Patrick Cockburn, The Independent, 14 September 2008
PBS NewsHour: "As Violence Peaks and Dips, Debate Over 'Surge' Persists" Archived 2014-01-18 at the Wayback Machine Debate between "surge" architect Fred Kagan and journalist Nir Rosen (March 11, 2008)
RAND Report, Counterinsurgency in Iraq: 2003–2006
Transcript and Audio mp3 and Video of Entire Address AmericanRhetoric.com
Transcript of the presidential speech on the official White House website.
Troop ‘Surge’ Took Place Amid Doubt and Debate by Michael R. Gordon, The New York Times, August 31, 2008.