BY NATHAN HODGE, LAURA MECKLER AND SUDEEP REDDY

WASHINGTON—The Obama administration is gearing up for this week's visit by Chinese Vice President Xi Jinping, expected to become the country's next leader, as a once-in-a-decade chance to set the tone in relations between Washington and Beijing.

But President Barack Obama starts the new relationship in a difficult setting, in the midst of a heated presidential contest that is exerting pressure on the president to accentuate a tough stance toward the Chinese. The White House has muffled expectations of major breakthroughs on any significant issue.

Nonetheless, the administration said it expects to zero in on some of the most contentious ...