The same poll shows support for Obama falling from 54 percent to 43 percent in Mexico, 35 percent to 28 percent in China, and 38 percent to 34 percent in Poland. A Pew Research Center survey this past spring backed up this finding, showing confidence in Obama's leadership plummeting 24 points in China since 2009 and 13 and 12 points in Mexico and Poland, respectively.
The Pew poll also showed that confidence in the president has fallen by 11 points in Japan and Spain, which perhaps explains why polling for these two countries is all over the place. Surveys that pit Obama against Romney have shown the president polling anywhere from 45 percent to 77 percent among Spaniards (polling in Portugal produces similar swings). BBC and UPI polls show Obama polling in the 30s in Japan, but 66 percent of Japanese respondents in the Pew poll said Obama should be reelected (Romney may not have improved his standing in Spain by using the country as a cautionary tale about fiscal irresponsibility during the first debate).
Romney, who's polling at 16 percent in Poland, has improved slightly on John McCain's popularity in the country in 2008 (Romney visited Warsaw during his overseas trip this summer and has accused the Obama administration of abandoning its Polish ally to appease Russia). But in China, the only country in Pew's survey that is following the 2012 election more closely than the 2008 race, Romney has not capitalized on Obama's declining support. Instead, Chinese news outlets and officials have repeatedly condemned "China-bashing" by both candidates. It's telling that while Obama is beating Romney 38-16 among Chinese participants in UPI's poll and 28-9 in the BBC's poll, half or more of the respondents in the surveys didn't express support for either candidate.
In the global context, it's helpful to think of swing states not as those that could break for either Obama or Romney but rather as countries where support for the candidates is tepid and where roughly half or more of the population wouldn't vote for either of the presidential aspirants. You could say these silent majorities are undecided, but the president and his Republican challenger are unlikely to win them over any time soon.