“Great Britain has already capitulated, so the Chinese have dismissed them,” said Anson Chan, a former top official in the Hong Kong government who has become a democratic activist. “But they do care — they especially care about what the United States says.”

A longtime democratic leader, Martin Lee, said the United States had a stake in the dispute that went beyond its usual commitment to democratic values. At the behest of China and Britain, it endorsed the 1984 joint declaration that guaranteed Hong Kong a high degree of autonomy and its own political system for 50 years after the handover.

“China cannot tell the U.S., ‘none of your business,’ because they lobbied for U.S. support for it,” Mr. Lee said, adding that China might feel emboldened to breach international agreements. In March, Mr. Lee and Mrs. Chan visited Washington to drum up American support for Hong Kong’s beleaguered democrats. They met with the House minority leader, Representative Nancy Pelosi of California, and with Senator Mark S. Kirk, Republican of Illinois, and they got a drop-in meeting with Vice President Joseph R. Biden Jr. That infuriated Chinese officials, some of whom suggested that the United States was fomenting unrest.

For the first time since 2007, Congress has reinstated an annual reporting requirement in the 1992 Hong Kong Policy Act, which mandates that the State Department assess the city’s progress.

Still, the melancholy reality for Hong Kong is that the White House, like 10 Downing Street, has other fish to fry with the Chinese. To date, the only official American response to the voting law is a statement from the State Department that “the United States supports universal suffrage in Hong Kong,” but refrains from criticizing the Chinese government.

Administration officials declined to speak on the record about Hong Kong before Ms. Rice’s visit. A spokesman for the national security adviser, Patrick Ventrell, said, “The administration remains committed to our rebalance to Asia, and that includes close and continuing consultation with top Chinese leadership directly from the White House.”

In sending Ms. Rice, the White House is seeking to revive a channel that was used by her predecessor, Tom Donilon, who met several times with Dai Bingguo, then China’s top foreign-policy official. Mr. Dai has been replaced by Yang Jiechi, a former foreign minister who is viewed as having less influence with the top leaders than Mr. Dai.