Coalition forces are not saying much, but the raids and arrests of Sunni Arabs and known Baath Party leaders are doing damage to the loose coalition of Saddam diehards who are organizing and funding the armed resistance. Stamping out this resistance is a long terms process that will eventually be turned over to Iraqi police. The Sunni resistance is, in effect, part of a centuries old civil war between Sunni Arabs, Shia Arabs and Sunni Kurds (plus several other smaller Islamic and Christian minorities.)
In the last week, US troops cracked down on militant Shias in Baghdad and Karbala. Attacks on US troops, and raids on Baath and al Qaeda hideouts continued in Sunni Arab neighborhoods.
The media gives a very distorted picture of this campaign. The military operations against the Baath Party are a long term operation, which will take a year or more pf raids, investigations and interrogations to round up the key leaders and paymasters driving the violence. Most weeks, there's simply nothing to report. The key mileposts are usually only recognized in hindsight, because only then is the exact composition of the opposition known, and which arrests and raids did the decisive damage.
Meanwhile, the Shia Arabs are going through their own civil war as more radical (and less well known and popular) religious leaders confront the more moderate (and older) clerics who are willing to work with the coalition. The Shia know they are the majority in the country and most believe that the coalition will supervise fair elections. At that point the Shia will be in charge; of the country and over a trillion dollars in oil reserves (11 percent of the world total). But the more radical Shia know they could not win an election, but they want to be in charge anyway. Some of these young clerics are inspired by Iran, where a minority of heavily armed Islamic conservatives dominate the majority and run the country as an "Islamic Republic." Coalition troops are caught in the middle of this attempt to set up an unpopular Islamic republic in Iraq.