Back in darkest days of the Cold War, when Americans and Russians faced the bleak specter of a decades-long struggle for global dominance and the distinct possibility of thermonuclear holocaust, geopolitical gamers often mused about playing the “China card.”

Were the U.S. to open diplomatic and trade relations with what was then called “Red China,” it was theorized, the presumed Chinese hunger for recognition and development capital would isolate the Soviet Union.

Richard Nixon, mired in Vietnam and facing a re-election campaign, played the card with his historic 1972 mission to China. It did, indeed, help push the Soviet Union towards eventual collapse, although the feat did not save Nixon from his own political demise two years later.

Since then, American politicians _ especially those whose standing with their own constituents has eroded _ have replayed the China card repeatedly, hoping that receiving the red carpet treatment abroad would polish their images at home.

California Gov. Arnold Schwarzenegger, whose usual game is chess, is playing Chinese checkers this week. He is seeking to regain traction after seeing his popularity cut in half and being hammered by voters in a special election he had called to lock down his control of the Capitol. He’s on a splashy tour of China whose ostensible purpose is to promote technological trade between California, whose $1.5 trillion economy is the fifth or sixth largest in the world, and China, which has become a fast-growing global powerhouse.

But Schwarzenegger, whose previous life as an international movie star makes him a big media draw, is not the only troubled Republican politician who’s playing the China card this week. Minnesota Gov. Tim Pawlenty’s public standing has slipped recently and he is facing a tough re-election next year. He is covering virtually the same China itinerary as Schwarzenegger, albeit with less media attention. And trailing the two governors is President Bush, whose public standing has been lacerated by the Iraq war and his administration’s sloppy handling of Hurricane Katrina’s destruction.

The cosmic interconnections among the three sojourning politicians, even beyond party and itineraries, are eerie.

Minnesotans elected Pawlenty three years ago as the successor to Jesse Ventura, a one-time wrestler and sometime actor whose astonishing election as a reform-minded outsider in 1998 foretold Schwarzenegger’s emergence in California. Ventura’s nosedive in popularity that drove him from office was an omen of Schwarzenegger’s rapid decline this year. Schwarzenegger and Ventura once appeared together in an action movie, but Ventura did a TV spot last year criticizing Schwarzenegger.

Pawlenty’s most likely opponent next year is Democratic Attorney General Mike Hatch, a slashingly partisan former state party chairman who bears an uncanny political resemblance to Schwarzenegger’s most likely foe, California Treasurer Phil Angelides, a slashingly partisan former state party chairman.

With his most recent setbacks, Schwarzenegger’s governorship continues on its parallel track with Bush’s presidency. While both were elected on their self-described ability to bridge cultural and ideological divisions (“I’m a uniter, not a divider,” Bush proclaimed) and make progress on such issues as education, both have become deeply divisive figures. That is largely because both launched wars that failed to resonate with their constituents.

Bush’s war was of the shooting variety, invading Iraq on the premise that it would remove a threat to American and global security, while Schwarzenegger’s pre-emptive strike was on the public employee unions he portrayed as being a threat to California’s economic prosperity. But their rationales have fallen out of favor, and so have they, as their sky-high standings with voters plunge to depths no politician likes to occupy. They have become targets not only for partisan rivals, but for editorial cartoonists, stand-up comedians, talking head pundits and other arbiters of the public’s mood.

It’s no wonder that President Bush and Governors Schwarzenegger and Pawlenty are traipsing through China this week. These days, the Chinese are much friendlier than their own voters.