In some areas of Iraq, too heavy a footprint hasn't been the problem. The lack of one has, but that may be changing in the wake of the president's recent Camp David meeting. From AP:
Hundreds of American and Iraqi troops backed by a U.S. gunship pushed into an insurgent-infested section of eastern Ramadi, expanding their campaign to bolster their presence in one of Iraq's most violent cities…. "It's one of the first steps to moving into areas of the city that have not had a large coalition or Iraqi presence for a long time, if ever," said Col. Sean MacFarland, commander of the 1st Brigade, 1st Armored Division that oversees the city.
This lack of a footprint has been a recurring theme. From a May 30, 2006 Washington Post piece:
...Marine officers on the ground have been open for more than a year now about needing more troops in Anbar, whose Sunni population, remoteness and comparative lawlessness have made it a stronghold for the insurgency. Anbar borders Syria, a conduit for some of the weapons, money and fighters.
From the April 26, 2006 Stars and Strips:
U.S. troops entered Mukhisa and the adjacent town of Abu Kharma on Sunday after hearing that the region is home to foreign fighters, members of Abu Musab al-Zarqawi's group and financiers behind roadside bomb and mortar attacks, said Lt. Col. Thomas Fisher, battalion commander.... One obstacle his troops face is that the two towns' contact with coalition forces over the past three years has consisted of three raids, in which hundreds of townspeople were arrested only to be released later, Fisher said. "When you neglect a town and don't engage the population, the terrorists who are here and the insurgents can tell them anything they want, and they will believe it because there is no one else telling them anything different," he said.
Nearly two years ago from the New York Times:
After the battle here in September [2004] the military left behind fewer than 500 troops to patrol a region twice the size of Connecticut. With so few troops and the local police force in shambles, insurgents came back and turned Tal Afar, a dusty, agrarian city of about 200,000 people, into a way station for the trafficking of arms and insurgent fighters from nearby Syria -- and a ghost town of terrorized residents afraid to open their stores, walk the streets or send their children to school. It is a cycle that has been repeated in rebellious cities throughout Iraq, and particularly those in the Sunni Arab regions west and north of Baghdad, where the insurgency's roots run deepest. ''We have a finite number of troops,'' said Maj. Chris Kennedy, executive officer of the Third Armored Cavalry Regiment, which arrived in Tal Afar several weeks ago. ''But if you pull out of an area and don't leave security forces in it, all you're going to do is leave the door open for them to come back. This is what our lack of combat power has done to us throughout the country. In the past, the problem has been we haven't been able to leave sufficient forces in towns where we've cleared the insurgents out.''