In drafting the United States Constitution, the Founding Fathers understood that, despite the checks and balances inherent to their concept of constitutional law, there would be instances when the president would need to act alone. That is why, despite the power to delcare war residing with the Congress, the president, as Chief Executive, alone is vested with the authority to send the armed forces into harm's way. An overseas crisis directly affecting American citizens and/or interests could not necessarily await the more deliberative process involved in debating and voting on a congressional resolution authorizing force -- a process that could take weeks.
A process of collective defense is similar. The United Nations was established to provide a forum in which disputes between states could be negotiated without a premature resort to force. The real authority in the United Nations, however, resides with the Security Council, which is comprised of 15 nations who serve for limited periods of time on a rotating basis. Five of those nations, however, are permanent members of the Security Council: The United States, Russia, China, France, and Great Britain. Those five, in addition to being permanent members of the council, also each have the authority to veto a U.N. resolution. In effect, only one of those five countries objecting to a proposed resolution is sufficient for the resolution to fail.
Because of the vast philosophical and ideological differences between those five countries -- especially, Russia and China on one side; the other three countries on the other -- attaining unanimity is extremely difficult. Consequently, by the time those five countries all agree on the wording of a resolution intended to resolve a crisis, hundreds of thousands of innocent lives can be lost to warfare.
Which brings us to the question of the conditions under which President Obama would pursue an unilateral course of action in response to a foreign policy crisis. All presidents react unilaterally when they deem it in the nation's vital national interest to do so. Neither Congress nor the absence of an international sanction will stop the president from pursuing an unilateral course of action if the alternative is delay at the expense of American lives. With respect to President Obama, his use of unmanned aircraft, or drones, to conduct air strikes inside the territory of Pakistan -- whether sometimes conducted with a "wink-and-a-nod" from Pakistan's government or not -- can be fairly categorized as an unilateral foreign policy. Similarly, the special forces mission to assassinate Osama bin Laden was done unilaterally, despite the violation of another country's territorial sovereignty.
One can only speculate about other types of policies or other actions President Obama might take unilaterally. There are myriad flashpoints around the world where violence could break out and to which President Obama may feel obligated to respond without U.N. authority an absent any allied country. Chinese military activities in the South China Sea, for example, could precipitate a crisis to which the United States would act alone. President Obama could also respond unilaterally to a conflict that suddenly arose in a part of Africa where American lives were at stake -- a situation similar to President Reagan's invasion of the Caribbean Island of Grenada in 1983.
In short, there are times when all presidents pursue a unilateral foreign policy.