The government is creating a new internal espionage agency, the General Security Directorate (GSD), that will specialize in infiltrating and destroying anti-government forces. Saddam Hussein had several organizations like this (so that they could keep an eye on each other), and some Saddam era security experts are apparently to be hired for the GSD. Coalition forces and the Iraqi police have already developed some informants inside, or close to, anti-government organizations. Information is the major shortcoming in the fighting against anti-government forces.
American troops can go wherever they want, and if they know where key anti-government people are, they can escort Iraqi police to make the arrest. There are fewer than a hundred people who are key to the anti-government forces. These include the Baath Party leaders who bankroll much of the activity (many of the violence is still performed by men paid to do it), and the small number of technicians who design and build many of the car bombs and road side bombs. American crime scene investigators have determined that there are only a few people out there designing and building these bombs, and if these bomb makers could be taken in, there would be a lot fewer bombs going off.
So the GSD will quickly rehire Saddam era security and espionage experts and recruit from among the large anti-resistance population in Sunni Arab areas. There is concern about hiring some of Saddams security people, for they all have blood on their hands. But the Iraqi government is more concerned with stopping the violence, which is a major concern for Iraqis in the major cities, especially Baghdad.
The government does have several battalion and company size Iraqi police and army units, carefully recruited and trained by American advisors, that are able and willing to fight wherever needed, including inside Iraqi cities. This gives the government the ability to go after hostile Iraqi forces no matter where they are. The government has signed into law martial law regulations, that allow for wide scale searches and detentions in areas declared out of control. That covers places like Fallujah and a few other Sunni Arab cities that have consistently resisted the new government, and openly demonstrated for the return of Saddam Hussein's government.
The interim government wants to root out the anti-government forces without triggering a civil war between Sunni Arabs and the other 80 percent of Iraqis. Hiring Sunni Arabs for the GSD and the elite army forces may do this, or it may not. The new security measures are going into effect immediately. So the answer will be known before the end of the Summer.