Governments can probably count on relatively widespread compliance for a short time, but draconian social distancing is not viable until the widespread availability of a vaccine. Leaders need to take action now so that once the caseload peaks and begins to decline, there is a glide path for people to return to a semblance of normal life.
Given that the ultimate fear is the strain on the medical system, there needs to be a multitiered strategy that attacks the problems of both supply and demand.
On the supply front, there all current shortages caused by the spike in COVID-19 virus cases must be addressed. Masks and other protective gear are scarce, which increases the risk of transmitting the disease to healthcare workers and thus exacerbating the problem of medical staffing. There is also a shortage of ventilators, which allow those with severe versions of the disease to keep breathing, giving them a fighting chance to live. In Italy and China, once medical systems reached their capacity, fatality rates soared. Increase capacity and our system can increase the number of severe cases it can treat before reaching that point.
On the demand side, we must focus on ways to slow the spread of the disease that do not depend on widespread lockdowns.