Just because you shutdown the country, doesn't mean that people will stop dying. It depends on velocity or steepness of the curve before you shut down. If you are driving 85MPH and you hit the brakes, does the car stop right away? Only the case numbers each day will start to go down after awhile when you let off the gas. It won't be right away but it will level off and eventually fall. It's happening in Italy which means the shutdown is obviously working. Here is Italy's curve of Daily New Cases.
People don't die as soon as they go to the hospital. Once people get sick, there is a huge queue of people that might take weeks to die. This is why you have to look at the resolved number as it means that patient has either survived or died. The bigger your queue of unresolved cases, the more people will die. For serious patients, roughly half will never come off a vent.
That's why you shutdown your country because if you don't you will get an exponential amount of people in your queue and not only will all of them die, all of people treating them will also die. Instead of going 85 MPH, you will keep increasing the speed of new cases at an exponential rate. It's like stepping on the gas and never letting up, which is what the USA was doing since end of January.
Even though the USA shut down, USA deaths per day will easily reach over 1000 deaths per day next week because of the people in the queue. By Easter, it will be doing around 2000 deaths per day. This is why you want to act quickly as possible because if you slow it down at the start, this shit would never take off. Every day you delay has almost a doubling effect. It's a lot easier to stop when you are going 5 MPH versus 100 MPH.
If you look at the USA numbers, they started off at a death rate of under 1% but as more cases are resolved, it has reached 1.6%. It will be the highest when the USA reaches its peak like Italy because the hospitals won't be able to support the case load.