and"who, contrary to your assertion, depend on popular support more than they themselves know"??
Its well known the 'manufactured consensus' (after Chomsky) by the elite controlled mass media/talk show hosts and that's why dala lama's clique was painted as some kind of saints with levitating ability. Another example is the vietnam war. The yanks pulled out not becos the elite yielded to the more popular anti-war sentiment but due to the fact they couldn't stop the VCs other than using nukes which is a different matters.
While china,which I fully agree is not a giant,one can't under-estimate the tentacles and the various hedgings schemes of the US elite. They support india mostly out of setting a 'democratic counterbalance' to china though the process mostly failed particularly during the hindu leaning to the russians and partly due to internal hindu failure. Hiding from sight is pointless though yankee attention could be diluted like IMO Bush Jr is an agent sent by Allah on behalf of Chairman Mao's entreaty. Another example was how the superpowerdom of the russians was perceived. According to article below,russian GDP/capita was once as low as 15% of the yanks(exactly wat chinese are at this moment.
http://akarlin.com/2012/06/the-soviet-economy-charting-failure/
The romans kept up the pretense of the empire towards its last years;the same with US and USSR. Wishing To be kept out of sight or to be luved is naive IMO