Chinese President Xi and President Obama are meeting after an interval with some changed context. President Obama is going into APEC meeting clearly as a diminished leader domestically and in last 2 years of his second term with a clear focus of leaving behind a workable strategy with China for his successor. On the other hand, President Xi has consolidated power in not so authentic manner domestically - by jailing his political opponents in arbitrary application of anti-corruption fight rather than undertaking long term, sustainable, institutional political reforms. (Xi is improving Chinese Legal System, but those reforms have just started and will be a while before anything concrete comes out.) President Xi has presided an economy which is not in any pink of health whereas President Obama continues to ride a reasonably recovering economy despite American Voters reluctance to consider otherwise.
The questions these two leaders will deal now are not much different than any earlier ones; primarily how to manage a peaceful growth of a new global power without resulting into any armed conflicts. Given stock of their respective domestic political capital, it seems that President Xi will be looking to continue his 'assertive' stance as far as claiming Chinese hegomoney in South China Sea whereas President Obama will be looking to find avenues where he can leave behind something useful for the next President to build upon.
Pundits talk about co-operation on Environment. That is all good and great from global perspective, but with American Politics having decisively moved with GOP, one is doubtful what lasting change can be achieved in dealing with China and rest of the world. President Obama did his EPA thing and it needs to be seen whether it can withstand corrupt courts of America. So this is all known by rest of the world. In essence, the world knows what President Obama can deliver on this front which is to say not much. Then why waste time and energy in engaging with vaporware? It will be prudent for President Obama to be circumspect in this regard, not to raise expectations and not promise anything which he cannot inherently deliver in next two years.
If at all Obama Administration wants to spend any capital (whatever it has) in working with Congress, the best it can do is to help Congress move on in changing IMF contributions so that China's gets bigger responsibility. That is the most sensible course of action as it will reduce incentive of China in going independent for a global developmental banker role as it gets that influence via IMF itself. Rest of the countries in Asia will be as well more willing to work with IMF rather than Chinese incarnation of ADB which is in essence Japan's financial power projection vehicle. Again, the trick for President Obama is to 'cast' Republican Opposition to IMF restructuring as a response which compromises America's national security.
The other area where the Congress might be more easy to work with will be in arming Vietnam which is asking for advanced weapons in order to prepare itself in a possible armed conflict with China. America's strategy should be to seek co-operation with China but not let go any opportunity to strengthen regional players. Working and deepening security alliances with as many players as possible around China, is one sure way of convincing China that raw power projections based on military might alone would not bring much benefits.
The same alliance strategy would be equally effective in entering into Free Trade Agreement with large number of Asian and South American countries without China. As most observers say, with a Republican Congress, Obama Administration should find it easy to move forward in this regard. In general coordinated actions in security and financial sectors will keep America's aggressive posture viable while extending the hand of co-operation to China. That is the standard 'sticks and carrots' policy President Obama has to execute in his last critical engagements with China.