By your logic, all of Chicago should be locked down, and a house to house search conducted.
We were all aware of the bombing in Boston, and that these guys killed a cop. That didn't make the searches reasonable or legally justified. That made a police presence in the community justified, and it may have justified a search that included visits to the front door of homes in that area, in the manner I described. Without any information that the bomber was in a particular house, there was no justification for forced entry into any houses, and especially for frisking the occupants. It was disgusting.
The fourth amendment says, "The right of the people to be secure in their persons, houses, papers and effects, against unreasonable searches and seizures, shall not be violated, nor shall warrant issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized." Our criminal law professor in law school, a lib, made us memorize this amendment. You may have your opinion about what it says, or what our policy should be in connection with a terrorist bombing in which 3 people were killed and dozens injured, but your opinion does not change the text or history of the 4th amendment. It does not allow what the police did in Watertown, and I am surprised that someone here would think it could.
Even in leftist California, when Dorner was running around in the mountains, the cops didn't do this to people. They respectfully went up to their cabins and checked for suspicious circumstances or odd behavior by the homeowners. They didn't treat them like foreign combatants. The people of Watertown were treated in the way the John Kerry described Iraqi jihadis being treated.
You're comparing apples to oranges. Not only does Wikipedia show that Chicago has a population under 3 million, Watertown over 30,000, but Chicago is arguably a war zone anyway. In other words, your neighbors in Watertown know when you sneeze. Chicago residents, on the other hand, probably hearing gunfire coming from all directions 24/7 and are probably somewhat desensitized to it.
Also, let's say Chicago law enforcement authorities have "all the time in the world" to obtain search warrants. So why isn't the constitutional process stopping street warfare in Chicago?