At the same time, certain foreign diplomatic initiatives can continue. Nixon initiated negotiations between Egypt and Israel that culminated, under Carter's administration, in the Camp David Accords. Truman tried to open negotiations with China, and the initiative's failure had little to do with opposition to a negotiated settlement in Korea.
The president has few domestic options. Whatever Obama does with his power domestically, Congress can vote to cut funding, and if the act is vetoed, the president puts Congressional Democrats in mortal danger. The place where he can act -- and this is likely the place Obama is least comfortable acting -- is in foreign policy. There, the limited deployment of troops and diplomatic initiatives are possible.
Obama's general strategy is to withdraw from existing conflicts in the Middle East and contain and limit Russian actions in Ukraine. The president has the ability to bring military and other pressure to bear. But the United States' opponent is aware that the sitting president is no longer in control of Washington, that he has a specific date of termination and that the more unpopular things he does, the more likely his successor is to repudiate them. Therefore, in the China-North Korea model, the assumption is that that continuing the conflict and negotiating with the successor president is rational. In the same sense, Iran chose to wait for the election of Ronald Reagan rather than deal with Jimmy Carter (who was not a failed president).
This model depends on the opponent's having the resources and the political will to continue the conflict in order to bargain with the president's successor, and assumes that the successor will be more malleable. This is frequently the result, since the successor can make concessions more readily than his predecessor. In fact, he can make those concessions and gain points by blaming the need to concede on his predecessor. Ironically, Obama used this strategy after replacing George W. Bush. The failed president frequently tries to entice negotiation by increasing the military pressure on the enemy. Truman, Johnson and George W. Bush all took this path while seeking to end their wars. In no case did it work, but they had little to lose politically by trying.
Therefore, if we follow historical patterns, Obama will now proceed slowly and ineffectively to increase military operations in Syria and Iraq, while raising non-military pressure on Russia, or potentially initiating some low-level military activities in Ukraine. The actions will be designed to achieve a rapid negotiating process that will not happen. The presidency will shift to the other party, as it did with Truman, Johnson and George W. Bush. Thus, if patterns hold true, the Republicans will retake the presidency. This is not a pattern unknown to Congress, which means that the Democrats in the legislature will focus on running their own campaigns as far away from Obama and the next Democratic presidential candidate as possible.
The period of a failed presidency is therefore not a quiet time. The president is actively trying to save his legacy in the face of enormous domestic weakness. Other countries, particularly adversaries, see little reason to make concessions to failed presidents, preferring to deal with the next president instead. These adversaries then use military and political oppositions abroad to help shape the next U.S. presidential campaign in directions that are in their interests.
It is against this backdrop that all domestic activities take place. The president retains the veto, and if the president is careful he will be able to sustain it. Obama will engage in limited domestic politics, under heavy pressure from Congressional Democrats, confining himself to one or two things. His major activity will be coping with Syria, Iraq and Russia, both because of crises and the desire for a legacy. The last two years of a failed presidency are mostly about foreign policy and are not very pleasant to watch.