The United States remains the world's number one economic and military power. This means that when President Obama sits down with many heads of state, the list of concerns that he presents is essentially a shopping list that he expects his counterpart to make good on. In many cases, the head of state of a country heavily dependent on the United States will have little choice but to deliver on the items on the list.
This is not true with China. While not yet the equal of the United States in either economic or military power, it is certainly a formidable enough power that the United States cannot simply dictate to it. This means that when it gives China a list of issues, it cannot reasonable expect China to agree to U.S. terms on all them. Therefore, when President Obama meets with China's President Hu Jintao this week, he will have to emphasize some things on the U.S. list while downgrading the importance of others.
For example, President Obama may emphasize enforcement of the patents and copyrights of U.S. companies like Pfizer and Microsoft. Or he may emphasize market access for financial service companies like Goldman Sachs and Citigroup. The emphasis on these issues may imply that concerns over items, like the value of the yuan, get less attention.
The issue of trade-offs is not mentioned in the NYT's stage setting for the meetings. This omission is striking since this priority setting obviously must be central in the administration's preparations. Surely the NYT could have contacted some experts on U.S.-China relations even if it could not find anyone in the administration who was prepared to discuss its priorities.