Cargo ships off Singapore’s coast on May 6. (Stephen Stromberg/The Washington Post)

SINGAPORE — Where you stand on fast-tracking the Trans-Pacific Partnership (TPP) trade deal is quickly becoming an ideological litmus test on the American left. But to some governments outside the United States, the TPP is already a litmus test of a much more consequential kind — of American seriousness in Asia.

The stakes in the TPP debate are a lot higher than the trade deal’s potential economic benefits. The view from Singapore, a trading partner and a party to TPP negotiations, is that this is “a critical moment,” Grace Fu, a senior Singaporean diplomat, told me last week. With Europe stagnating and China slowing, the world needs an engine of growth. Will the United States lead the effort to make itself and its trans-Pacific partners more prosperous, in the process anchoring itself in Asia and cementing its future relevance? Or will the United States shrink from its traditional role of promoting international commerce and cooperation, sending the message that it won’t commit to the region, even as China invests in countries across the continent?

The Senate chose not to commit on Tuesday, refusing to begin debate on a bill that would give President Obama fast-track authority needed to finish TPP negotiations. Thankfully, this is not the final word on the matter. But even if fast track eventually passes, and after it the final TPP agreement, the Senate has already sent exactly the wrong message.

“At the end of the Cold War, America was the only hyper-power in the world, so there was no question about American leadership,” Vivian Balakrishnan, a top Singaporean minister, said in an interview with me. “But obviously things are changing. … That brief interlude when you were the only game in town is not going to be the situation going forward.”

Many in Asia still look up to the United States. But, “We always worry about the American impulse to look inwards,” Balakrishnan said. “We worry about the American interest in looking beyond its shores, and whether in fact there is even a bit of fatigue from decades of war with apparently inconclusive outcomes, and whether that has sapped the American sense of determination. And the problem with that sort of doubt, self-doubt, is that after a while even your friends start to wonder whether you still have that commitment, that zeal, that passion, that energy to project yourself and what you believe in to the rest of the world.”

Rather than allaying them, the Senate stoked these fears on Tuesday, in large part because of Elizabeth Warren and Bernie Sanders-style opposition to fast-track that’s based on dead-end, anti-trade ideology and hyperbole about trade deals’ potential drawbacks. If Congress kills the TPP, other nations would doubt American levelheadedness and reliability, and they would have good reason.

But they wouldn’t stand still. Countries will continue to make deals with one another, with or without the United States. “We can’t afford to wait for everyone to get on board,” Balakrishnan said. “We have to try to do as much as we can to run as fast as we can.” If only the Senate had a similar sense of urgency and responsibility.

Update, 10:34 a.m.: Text above slightly edited for clarity.