Apparently not at the Washington Post. It ran an article projecting a severe shortage of doctors due to the retirement of large numbers of baby boomers. The article never discussed the possibility of allowing more foreign doctors into the country.
The current rules on foreign doctors are highly protectionist to ensure that doctors can command high salaries. However, if shortages become too severe, the country could easily opt to relax these rules. There is no shortage of smart and ambitious kids in the developing world who would eagerly seize the opportunity to train to U.S. standards and work as doctors in the United States. This flow could easily meet any future demand for doctors in the United States.
It would also be a simple matter to attach a tax to the earnings of these doctors that would be paid to the home country. This tax could be used to train 2-3 doctors for every doctor that practices in the United States, thereby ensuring that the health care in developing countries improves by this arrangement as well.
Remarkably the Post does not discuss the possibility of increased use of foreign physicians even though it is almost fanatical in its support of free trade in other circumstances.