The 4th was incorporated in the 60's. All the cases were specific individuals (e.g. Terry stop) or cars or houses. Houses have the most protection. Any unrelated criminal case arising from Watertown (e.g. if the cops had found drugs after busting into someone's house) would be laughed out of court. There is simply no case law supporting home searches with the few exceptions that only apply to specific houses. The cop must pursue a suspect into a specific house. A cop may have a hunch about a specific house and that is legal grounds (has to be explicit). A cop might see something in the yard or through a window which would make the search legal. Or the cops can get permission from a homeowner or any representative (essentially anyone from a teenager on up can legally let them in). But that is it.
That is called "articulable grounds for suspicion", and a cop has to have them to have probable cause for a search or seizure. Still have to have a warrant, except in exigent circumstances.