The big problem as people see it is that the majority population of iraq is Shiite.
When Saddam was in charge, the Sunni minority ran things.
Now, with the Shiites in power, in a collapsed state, the natural progression would be a closer relationship and dependence on Iran, a predominately Shiite country, just next door. Some people (Israel) is fearful of such an inevitability, because it wants to remain the dominant economic power in the region. Iran & Iraq were the two dominant players in the region, and by keeping the two nations at war with each other in the 80's, they stalled their progress as individual nations. After the decimation visited upon Iraq followed by sanctions, Iraq went downhill, while Iran was doing it's thing as a nation. Now the failed Iraqi invasion simply hastens the solidification of the region that the Iran / Iraq wars were designed to prevent. A newly emerged, peaceful, prosperous nation called the Islamic Republic of Iranq (Iran/Iraq) strikes terror through the hearts of zionists and those with designs on middle eastern oil.
Sooner or later, all those countries are going to be more united in their desire to lives free prosperous and safe lives, ...and when that happens, I'd hate to be an American member of the military stationed in that area.
Eventually, they will set aside their differences to focus on their common goals. It wouldn't be the first time it has happened, ...although Iran appears to hate certain Arab countries more than it hates Israel.