General Engagement with China
Despite the public's cool feelings toward China, a majority generally favors engaging China diplomatically and economically.
Despite a somewhat negative view of China, as a general rule, a majority prefers a policy of constructive engagement with Beijing. This holds true when Americans are asked separately about economic and diplomatic engagement, though majority support for trade has recently diminished. Seventy-five percent supported having diplomatic relations, and 63% favored trade with China in CCFR’s June 2004 poll. This was down from 80% for diplomatic relations and 71% for trade in June 2002. 
These general attitudes in favor of engagement are long-standing. In a May 1999 Time/CNN poll, for example, 58% said they think it "it's better for the United States…to engage [China] economically" rather than to "be more confrontational with China." Twenty-nine percent preferred a more confrontational approach.  When asked in a March 1997 Frederick Schneiders poll if they simply support or oppose "developing closer political and economic ties with China," 61% supported doing so, while only 32% opposed the idea. 
At the same time the idea of using constraints on economic engagement as a way to try to influence China hold some attraction. An NBC/Wall Street Journal poll from July 2005 offered two statements about the US-China relations. Nearly half (47%) agreed that “We should demand that China improve its military policies if China wants to continue to enjoy its current trade status with the US,” while a slightly smaller proportion (44%) agreed that “We should maintain good trade relations with China, despite disagreements we might have with its military policies.”  Also, a majority wants labor and environmental standards to play a stronger part in US trade with China. Fifty-eight percent said such protections should be “enforced” in November 2004 (Democracy Corps). When offered a list of countries including China, a bare majority (51%) favored “the use of economic sanctions” on China.(Chicago Council on Foreign Relations, June 2002).
In the 1990s Americans showed support for engagement with China. An example was the steady support for President Clinton's visit to China in 1998. Several polls by Gallup and others in June and July 1998 found majorities of at least 55% saying they approved of Clinton's decision to visit China. This is significant, in that a substantial majority favored Clinton's trip even though Congress was actively investigating allegations of Chinese donations to Clinton's 1996 campaign. Both ABC News and CBS/New York Times polls in June 1998 found a majority (68% and 59%, respectively) saying that Clinton should go "because of the need to maintain good relations with the Chinese, and to open China's markets to US companies." In both cases, less than a third of respondents felt "he should not go while these questions about political donations are being investigated." Also, a June 1998 NBC/Wall Street Journal poll found a plurality continued to support Clinton's trip (48% to 42%) even when it was noted that he would participate in a welcoming ceremony in Tiananmen Square, "the site of pro-democracy demonstrations in 1989 that ended in the death of several hundred demonstrators." Support for the trip remained strong even though the public did not believe that it would "significantly improve US relations with China" (42% yes, 48% no) or "significantly improve China's treatment of its citizens" (20% yes, 70% no). Polls taken after Clinton's return showed that it was perceived as somewhat more successful than expected.
A final instance of public acceptance of ups and downs in the US-China relations was the US bombing of the Chinese embassy in Belgrade during the NATO air campaign to stop Serb aggression in Kosovo. The US said the bombing was a mistake and apologized for it, but the Chinese government did not accept this explanation and thousands of Chinese protested in Beijing. The US public clearly empathized with the Chinese. A May 1999 CBS News survey found that although a strong majority of Americans (61%) felt that the US apology for the bombing was "enough" and the US did not need to "say more" to the Chinese, an even larger majority (66%) said that the response in China was "understandable." In addition, while a majority felt that US relations with China would be damaged, May 1999 Newsweek and Pew surveys found that only about 1 in 4 believed it would cause "permanent" or "long-lasting" damage. This is roughly the same percentage that told Los Angeles Times pollsters in March 1999 that any "US and NATO air strikes on Kosovo" would "cause permanent damage" to US relations with "Russia and China."