To answer your question: Yes, the police have the right to enter any home without a warrant to arrest a criminal, but only if they are in "hot pursuit." This has been the law for hundreds of years, steming from the ancient common law of England. The definition of hot pursuit can vary from juridiction to jurisdiciton, but basically it is defined as being in the act of pursuing a felon, with little or no break in visual or other "contact" with the fleeing felon during the apprehension.
I understand that Dee is a retired office, so he may be able to give you the definition that was taught to him as an officer.
And by the way, game wardens enjoy a very special right of entry. They have the right to enter any premises to search for illegally taken game, if they have probable cause to believe it is there, without ever getting any warrant from a judge or other judicial authority. They do not have to be in hot pursuit. This too has been the law for hundreds of years, arising from English common law.
Seriously, I think you guys should be more concerned with coronary disease, obesity, diabetes, high blood pressure, cancer and lyme disease that this silly diatribe as to some fictional authority, in a time of emergency, ordering you to stay in your house for a while. Nobody ordered anybody to do anything in Boston. They only asked and urged.
And yes, the President and all Governors have the right to declare martial law. And yes, if the Governor of Massachusetts had wanted to, he could have declared martial law. It is a discretionary versus ministerial governmental act, and is there not subject to review by other politicos or people.
Regards, Mannyrock