Nature of the US-China Relationship
Americans are more apt to view the US-China relationship as unfriendly than friendly, but only a small minority views China as an outright enemy. Americans are divided as to whether China is cooperating with the US in the war on terrorism. A strong majority views relations with China as being important to US interests and growing more important, though problems posed by China are not considered pressing.
While not viewed directly as an enemy of the United States, perceptions of China’s foreign policy influence on the United States are predominantly negative. Asked in April 2006 about how they view “the effect of Chinese foreign policy on the United States and its interests,” a majority of 54% said it has been very or somewhat negative, while only 36% say it has been positive. 
For decades Harris polls have asked whether Americans think China is "an ally of the US, is friendly but not an ally, is not friendly but not an enemy, or is unfriendly and is an enemy of the US." Gallup, the Los Angeles Times, CBS News and others have used similar questions. Over the last few years, with just a few exceptions, a plurality to fairly strong majority have said that China is either "not friendly" or an enemy. Most recently (August 2005) Harris found a 53% saying China was either "not friendly, but not an enemy" (38%) or “unfriendly and…an enemy of the US (15%), while 41% called it either a "close ally" (5%) or "friendly but not a close ally" (36%).
There has been significant fluctuation on this question and it is natural to try to look for a relationship between these fluctuations and events in the news. However, doing so is questionable because some of the more extreme numbers have been nearly contiguous. A marked example is that the highest percentage characterizing China as unfriendly or an enemy was found in an April 20-22, 2001 poll by CNN/USA Today. Coming on the heels of the spy plane incident, it is tempting to assume that this high number was due to residual resentment about the incident. However, a CBS News poll taken immediately after on April 23-25 found one of the lowest percentages ever recorded (44%) characterizing China as unfriendly or an enemy. Therefore, it appears that this question, while consistently showing a predominantly cool attitude on the part of the public, nonetheless elicits unstable results.[2a]
Though Americans lean toward seeing the relationship in unfriendly terms, very few see China as an enemy. The highest percentage giving such a characterization over the last years was 27% in August 2000. Also, when given just three choices, as in several recent Pew surveys, very few choose the option that depicts China as an enemy, while a plurality or majority tends to gravitate to the middle option. Most recently, in July 2004 Pew found that just 14% thought of China as an "adversary," while 40% preferred to think of it as a "serious problem but not an adversary" and 36% felt China is "not much of a problem."[2b] This is a bit warmer than when Pew asked this question in May 2001 and found that 19% thought of China as an "adversary," 51% said a "serious problem but not an adversary" and 22% felt China is "not much of a problem"—a 14 point increase for the most sanguine position.
However, when forced to choose between just two options of characterizing China--as either an adversary or an ally--a strong majority chooses the former. As recently as July 2005, a NBC/Wall Street Journal poll found 49% that thought of China as more of an adversary “in general”, while just 26% saw it as more of an ally. An NBC/Wall Street Journal poll found that about 3 in 4 considered China to be "an adversary and competitor" on "diplomatic and military issues" (77%) as well as "economic issues" (73%).  When asked in a May 1999 Pew poll, 51% disagreed with the assertion that "China is basically friendly toward the United States" (41% agreed).
Similarly, over the years the public has tended to see US-China relations as less than exemplary and with little movement, positive or negative. In a May 1998 ABC News poll, a very strong majority described bilateral relations as "only fair" (54%) or "poor" (21%). Just 21% felt relations were "excellent" or "good." Pew surveys between 1995 and 2000 found majorities saying that "relations between the US and China" have been "staying about the same," as opposed to getting better or worse. However, in May 2001 those choosing "staying about the same", while still a plurality, fell to 48% from 55% in March 2000. The percentage saying relations are "getting worse" more than doubled, from 19% to 40%, and those who felt relations are "improving" declined to from 13% to 6%. This seems to have been evidence of a downward blip as a result of the spy plane incident in early 2001. Similar responses were recorded in June 1999, on the heels of the controversy over Chinese spying in US nuclear labs. By July 2004 responses to the same question were similar to those of 2000, with 58% saying relations were staying about the same.
Again, it is striking--when one looks at long-term trend questions on China's relationship to the US--to see the dramatic shift in overall views of China since the June 1989 crackdown on pro-democracy demonstrators in Tiananmen Square. The data are unfortunately somewhat patchy -- the Harris question mentioned above was not asked between 1988 and 1994 - but there seems to be no doubt that the events of 1989 did serious damage to Americans' view of the US-China relationship. In May 1988, Americans Talk Security found that a 59% majority felt that China was an "ally" (9%) or "friendly" to the US (50%).[7a] With just one exception between 1979 and 1988, strong pluralities or slim majorities thought of China as an ally or as a friendly country; in each case, more than 40% viewed China as "friendly." However (as discussed above) since 1994, when organizations began to ask the question again, pluralities or majorities have viewed China as "unfriendly" or an "enemy."
To cite another example, a Roper poll question used frequently in the 1980s offered respondents five options to describe China ranging from "ally" to "enemy" with "neutral" at the midpoint. In each case between 1982 and 1987 only 19-29% characterized China as an enemy or as unfriendly. But when Potomac Associates and Opinion Dynamics dusted off this question in June 1999, the results were dramatically different: 46% referred to China as "unfriendly" or an "enemy."
Unsure Whether China Is Helping in the War on Terrorism
Americans are divided on the question of whether China is helping the US in the war on terrorism. In June 2002 CCFR asked whether a number of countries were “reliable partners of the US” against terrorism. Only 41% saw China as very (5%) or somewhat (36% reliable); 47% saw it as somewhat (28%) or very (19%) unreliable. When a September 27-28, 2001 Time/CNN poll asked whether "the United States can…count on" China "to help combat terrorism"; 46% thought China could be counted on, and 43% thought it could not be. (By way of comparison, in the same poll 90% thought the US could count on Britain, 70% thought the same for Russia, and 42% thought the same for Saudi Arabia.)
On September 20-21 Newsweek also offered a list of countries and asked, "Are they doing what the Bush Administration is asking of them, or not?" Thirty-eight percent thought China was responding to US requests, 30% thought China was not responding, and 32% did not give an answer. (Again, for comparison, in the same poll 76% thought "our European allies" were responding, 53% thought the same for Russia, and 28% thought the same for "Arab and Muslim countries.") [9a] Thus the public sees China's partnership in the war on terrorism as less than reliable. These results are quite consistent with the public's broader attitude that the US- China relationship lies somewhere between friendly and unfriendly territory.
On the separate matter of taking military action against Iraq in 2003, two-thirds of Americans (67%) correctly thought in January 2003 that “the United States cannot count on the support of…China” “in planning for an invasion, while 22% thought it could (CNN/USA Today).[9b]
China as Important to US Interests
Many recent polls have found that a strong majority believes events in China and relations with China are important to US interests, especially as China’s stature on the global scale grows. This is partly because Americans see the great improvement in relations with China over the past three decades as important to bringing the Cold War to an end. In a June 2004 poll, respondents were offered a list of six important events, described as “foreign policy successes” of the US, and asked which one they thought was the most important. A large plurality—45%--said “increased cooperation between the US and Cold War enemies like Russia and China” was the most important; no other item garnered more than 19% (PBS).
A strong majority also shares the belief that the US has "vital interests" in China - and this attitude has grown substantially stronger over the past decade. The quadrennial CCFR poll on foreign policy issues, found that the percentage saying the US has a "vital interest" in China rose from 47% in 1990 to 68% in 1994, 74% in 1998, and 83% in 2002.  In a June 1999 poll by Potomac Associates and Opinion Dynamics, which used the same question but offered four (rather than two) response options, that percentage rose again, to 78% (very strong and fairly strong vital interest, combined). [11a]
Though Americans see China as having an unfriendly relationship with the US, most Americans have not seen China as a very serious threat to the US in recent years. In a January 2003 Time/CNN survey, for example, only about a fifth (22%) considered it "very serious," though 35% said they considered China a "moderately serious threat." Forty percent considered China a "slight threat" or "not a threat." 
In comparison to other countries, China is not seen as posing a compelling problem for the US. In February 2005, given a list of countries--including North Korea, Iraq, Israel and the Palestinians, China, and Iran-- respondents were asked to evaluate which posed the most important “foreign policy issue” (CBS/New York Times). China was seen as most important by only 4%--the lowest percentage of any country. The highest was Iraq at 54%.  This is in contrast to a poll done in a July 2001 ABC News poll that asked respondents "to name one nation that you might consider the greatest threat to world peace": 35% named China (13% chose Iraq, 10% Russia). [See footnote for other examples].  This represented a clear shift after 1990 and the end of the Cold War--away from concern about the USSR/Russia and toward concern about China as the primary threat to the US.