Ex- Deputy Secretary of State’s Book on China

choi

Ali Wyne, The New Special Relationship; China's conception of its core interests has expanded beyond Taiwan and Tibet to include the Spratly Islands and the Senkakus. Wall Street Journal, June 27, 2014
online.wsj.com/articles/book-review-strategic-reassurance-and-resolve-by-james-steinberg-and-michael-e-ohanlon-1403822687
(book review on James Steinberg and Michael E O’Hanlon, Strategic Reassurance and Resolve; US-china relations in the twenty-first century. Princeton University, Press 2014)

Note:
(a) James Steinberg
en.wikipedia.org/wiki/James_Steinberg
(1953- ; Deputy Secretary of State Jan 28, 2009-July 28, 2011)

(b) “The authors concede that the success of strategic reassurance will ultimately depend upon ‘the extent to which China and the United States mutually believe that it is possible to accommodate what the other perceives as its vital national interest in ways that are consistent with its own.’ It has proved difficult, however, to ascertain the precise contours of China's core interests.”

Regarding the internal quotation. Each country (China and US) “accommodate * * * in ways that are consistent with its own [vital national interest]”: this is the framework of the sentence.
"Having anchored the international system for the past seven decades, the US will find it psychologically exacting to accommodate China's desire for a coequal role. It is possible, of course, that China will never achieve parity with the U.S. The US cannot, however, afford to conduct a foreign policy that assumes—or, worse, requires—the impossibility of such an outcome."
(i) anchor (vt): "to act or serve as an anchor for <it is she who is anchoring the rebuilding campaign — GD Boone> <anchoring the evening news>"
www.merriam-webster.com/dictionary/anchor
(ii) "assumes—or, worse, requires—the impossibility of such an outcome"

It means that US should not shut the door of power-sharing with China, at least a bit.